SlideShare a Scribd company logo
Recall that the Fibonacci and Lucas sequences Fn and Ln are (0, 1, 1, 2, . . . ) and (2, 1, 3, 4, . . .
), respectively. Given that x0 = x1 for the sequence xn in part (d), show that the ratio xn/(Fn +
Ln) does not depend on n.
where part (d) gives xn = xn?1 + xn?2 where n >= ?? 2.
Solution
Sequence in part (d) is given by (x0, x0, 2x0, 3x0, 5x0,8x0,....) = x0(1,1,2,3,5,8,....)
Fn + Ln = (2,2,4,6,10,....) = 2(1,1,2,3,5,8,....)
So clearly if we divide the nth term of xn and Fn+Ln then we get xn/(Fn+Ln) = x0/2 which does
not depend on n

More Related Content

More from arihantmobileselepun

Create a java project that - Draw a circle with three random init.pdf
Create a java project that - Draw a circle with three random init.pdfCreate a java project that - Draw a circle with three random init.pdf
Create a java project that - Draw a circle with three random init.pdf
arihantmobileselepun
 
aphase The spindle contracts and the sister chromatids are separated.pdf
aphase The spindle contracts and the sister chromatids are separated.pdfaphase The spindle contracts and the sister chromatids are separated.pdf
aphase The spindle contracts and the sister chromatids are separated.pdf
arihantmobileselepun
 
A population of wild deer mice includes individuals with long or sho.pdf
A population of wild deer mice includes individuals with long or sho.pdfA population of wild deer mice includes individuals with long or sho.pdf
A population of wild deer mice includes individuals with long or sho.pdf
arihantmobileselepun
 
Who is it important that the lymphatic system operate separately f.pdf
Who is it important that the lymphatic system operate separately f.pdfWho is it important that the lymphatic system operate separately f.pdf
Who is it important that the lymphatic system operate separately f.pdf
arihantmobileselepun
 
Provide a full explanation to the below question.1. Summarize the .pdf
Provide a full explanation to the below question.1. Summarize the .pdfProvide a full explanation to the below question.1. Summarize the .pdf
Provide a full explanation to the below question.1. Summarize the .pdf
arihantmobileselepun
 
Write a program to generate the entire calendar for one year. The pr.pdf
Write a program to generate the entire calendar for one year. The pr.pdfWrite a program to generate the entire calendar for one year. The pr.pdf
Write a program to generate the entire calendar for one year. The pr.pdf
arihantmobileselepun
 
Write the interval notation for the set of numbers graphed. Solu.pdf
Write the interval notation for the set of numbers graphed.  Solu.pdfWrite the interval notation for the set of numbers graphed.  Solu.pdf
Write the interval notation for the set of numbers graphed. Solu.pdf
arihantmobileselepun
 
Hyenas are diploid organisms, and their gametes contain 20 chromosome.pdf
Hyenas are diploid organisms, and their gametes contain 20 chromosome.pdfHyenas are diploid organisms, and their gametes contain 20 chromosome.pdf
Hyenas are diploid organisms, and their gametes contain 20 chromosome.pdf
arihantmobileselepun
 
Why doesnt hemoglobin have any intermediate conformations between .pdf
Why doesnt hemoglobin have any intermediate conformations between .pdfWhy doesnt hemoglobin have any intermediate conformations between .pdf
Why doesnt hemoglobin have any intermediate conformations between .pdf
arihantmobileselepun
 
4. What is gyanandromorphy How does this happenSolutionAnswe.pdf
4. What is gyanandromorphy How does this happenSolutionAnswe.pdf4. What is gyanandromorphy How does this happenSolutionAnswe.pdf
4. What is gyanandromorphy How does this happenSolutionAnswe.pdf
arihantmobileselepun
 
Which of the following requires the mitochondria to create contact po.pdf
Which of the following requires the mitochondria to create contact po.pdfWhich of the following requires the mitochondria to create contact po.pdf
Which of the following requires the mitochondria to create contact po.pdf
arihantmobileselepun
 
why nitrogen fixation is so importantSolutionNitrogen fixation.pdf
why nitrogen fixation is so importantSolutionNitrogen fixation.pdfwhy nitrogen fixation is so importantSolutionNitrogen fixation.pdf
why nitrogen fixation is so importantSolutionNitrogen fixation.pdf
arihantmobileselepun
 
what will happen to the photon if two photons enter the same atom si.pdf
what will happen to the photon if two photons enter the same atom si.pdfwhat will happen to the photon if two photons enter the same atom si.pdf
what will happen to the photon if two photons enter the same atom si.pdf
arihantmobileselepun
 
Which of the following is not a function of the skeletonA. Storag.pdf
Which of the following is not a function of the skeletonA. Storag.pdfWhich of the following is not a function of the skeletonA. Storag.pdf
Which of the following is not a function of the skeletonA. Storag.pdf
arihantmobileselepun
 
3. Which of the following will completely dissolve in water (More t.pdf
3. Which of the following will completely dissolve in water (More t.pdf3. Which of the following will completely dissolve in water (More t.pdf
3. Which of the following will completely dissolve in water (More t.pdf
arihantmobileselepun
 
True or False-A correlational study is used to examine the relatio.pdf
True or False-A correlational study is used to examine the relatio.pdfTrue or False-A correlational study is used to examine the relatio.pdf
True or False-A correlational study is used to examine the relatio.pdf
arihantmobileselepun
 
what are some good current research proposal topic in psychology..pdf
what are some good current research proposal topic in psychology..pdfwhat are some good current research proposal topic in psychology..pdf
what are some good current research proposal topic in psychology..pdf
arihantmobileselepun
 
The following diagram shows nondisjunction In either Melosis I or Mel.pdf
The following diagram shows nondisjunction In either Melosis I or Mel.pdfThe following diagram shows nondisjunction In either Melosis I or Mel.pdf
The following diagram shows nondisjunction In either Melosis I or Mel.pdf
arihantmobileselepun
 
Save Write a program to implement Binary search using recursive algo.pdf
Save Write a program to implement Binary search using recursive algo.pdfSave Write a program to implement Binary search using recursive algo.pdf
Save Write a program to implement Binary search using recursive algo.pdf
arihantmobileselepun
 
1. Which of the following is responsible for problem-solving skills .pdf
1. Which of the following is responsible for problem-solving skills .pdf1. Which of the following is responsible for problem-solving skills .pdf
1. Which of the following is responsible for problem-solving skills .pdf
arihantmobileselepun
 

More from arihantmobileselepun (20)

Create a java project that - Draw a circle with three random init.pdf
Create a java project that - Draw a circle with three random init.pdfCreate a java project that - Draw a circle with three random init.pdf
Create a java project that - Draw a circle with three random init.pdf
 
aphase The spindle contracts and the sister chromatids are separated.pdf
aphase The spindle contracts and the sister chromatids are separated.pdfaphase The spindle contracts and the sister chromatids are separated.pdf
aphase The spindle contracts and the sister chromatids are separated.pdf
 
A population of wild deer mice includes individuals with long or sho.pdf
A population of wild deer mice includes individuals with long or sho.pdfA population of wild deer mice includes individuals with long or sho.pdf
A population of wild deer mice includes individuals with long or sho.pdf
 
Who is it important that the lymphatic system operate separately f.pdf
Who is it important that the lymphatic system operate separately f.pdfWho is it important that the lymphatic system operate separately f.pdf
Who is it important that the lymphatic system operate separately f.pdf
 
Provide a full explanation to the below question.1. Summarize the .pdf
Provide a full explanation to the below question.1. Summarize the .pdfProvide a full explanation to the below question.1. Summarize the .pdf
Provide a full explanation to the below question.1. Summarize the .pdf
 
Write a program to generate the entire calendar for one year. The pr.pdf
Write a program to generate the entire calendar for one year. The pr.pdfWrite a program to generate the entire calendar for one year. The pr.pdf
Write a program to generate the entire calendar for one year. The pr.pdf
 
Write the interval notation for the set of numbers graphed. Solu.pdf
Write the interval notation for the set of numbers graphed.  Solu.pdfWrite the interval notation for the set of numbers graphed.  Solu.pdf
Write the interval notation for the set of numbers graphed. Solu.pdf
 
Hyenas are diploid organisms, and their gametes contain 20 chromosome.pdf
Hyenas are diploid organisms, and their gametes contain 20 chromosome.pdfHyenas are diploid organisms, and their gametes contain 20 chromosome.pdf
Hyenas are diploid organisms, and their gametes contain 20 chromosome.pdf
 
Why doesnt hemoglobin have any intermediate conformations between .pdf
Why doesnt hemoglobin have any intermediate conformations between .pdfWhy doesnt hemoglobin have any intermediate conformations between .pdf
Why doesnt hemoglobin have any intermediate conformations between .pdf
 
4. What is gyanandromorphy How does this happenSolutionAnswe.pdf
4. What is gyanandromorphy How does this happenSolutionAnswe.pdf4. What is gyanandromorphy How does this happenSolutionAnswe.pdf
4. What is gyanandromorphy How does this happenSolutionAnswe.pdf
 
Which of the following requires the mitochondria to create contact po.pdf
Which of the following requires the mitochondria to create contact po.pdfWhich of the following requires the mitochondria to create contact po.pdf
Which of the following requires the mitochondria to create contact po.pdf
 
why nitrogen fixation is so importantSolutionNitrogen fixation.pdf
why nitrogen fixation is so importantSolutionNitrogen fixation.pdfwhy nitrogen fixation is so importantSolutionNitrogen fixation.pdf
why nitrogen fixation is so importantSolutionNitrogen fixation.pdf
 
what will happen to the photon if two photons enter the same atom si.pdf
what will happen to the photon if two photons enter the same atom si.pdfwhat will happen to the photon if two photons enter the same atom si.pdf
what will happen to the photon if two photons enter the same atom si.pdf
 
Which of the following is not a function of the skeletonA. Storag.pdf
Which of the following is not a function of the skeletonA. Storag.pdfWhich of the following is not a function of the skeletonA. Storag.pdf
Which of the following is not a function of the skeletonA. Storag.pdf
 
3. Which of the following will completely dissolve in water (More t.pdf
3. Which of the following will completely dissolve in water (More t.pdf3. Which of the following will completely dissolve in water (More t.pdf
3. Which of the following will completely dissolve in water (More t.pdf
 
True or False-A correlational study is used to examine the relatio.pdf
True or False-A correlational study is used to examine the relatio.pdfTrue or False-A correlational study is used to examine the relatio.pdf
True or False-A correlational study is used to examine the relatio.pdf
 
what are some good current research proposal topic in psychology..pdf
what are some good current research proposal topic in psychology..pdfwhat are some good current research proposal topic in psychology..pdf
what are some good current research proposal topic in psychology..pdf
 
The following diagram shows nondisjunction In either Melosis I or Mel.pdf
The following diagram shows nondisjunction In either Melosis I or Mel.pdfThe following diagram shows nondisjunction In either Melosis I or Mel.pdf
The following diagram shows nondisjunction In either Melosis I or Mel.pdf
 
Save Write a program to implement Binary search using recursive algo.pdf
Save Write a program to implement Binary search using recursive algo.pdfSave Write a program to implement Binary search using recursive algo.pdf
Save Write a program to implement Binary search using recursive algo.pdf
 
1. Which of the following is responsible for problem-solving skills .pdf
1. Which of the following is responsible for problem-solving skills .pdf1. Which of the following is responsible for problem-solving skills .pdf
1. Which of the following is responsible for problem-solving skills .pdf
 

Recently uploaded

Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
Dr. Mulla Adam Ali
 
Temple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation resultsTemple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation results
Krassimira Luka
 
B. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdfB. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdf
BoudhayanBhattachari
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
Priyankaranawat4
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Himanshu Rai
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
TechSoup
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Fajar Baskoro
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
Wahiba Chair Training & Consulting
 
Constructing Your Course Container for Effective Communication
Constructing Your Course Container for Effective CommunicationConstructing Your Course Container for Effective Communication
Constructing Your Course Container for Effective Communication
Chevonnese Chevers Whyte, MBA, B.Sc.
 
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Nguyen Thanh Tu Collection
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
heathfieldcps1
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
Jyoti Chand
 
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Leena Ghag-Sakpal
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Nguyen Thanh Tu Collection
 
math operations ued in python and all used
math operations ued in python and all usedmath operations ued in python and all used
math operations ued in python and all used
ssuser13ffe4
 
How to deliver Powerpoint Presentations.pptx
How to deliver Powerpoint  Presentations.pptxHow to deliver Powerpoint  Presentations.pptx
How to deliver Powerpoint Presentations.pptx
HajraNaeem15
 
Mule event processing models | MuleSoft Mysore Meetup #47
Mule event processing models | MuleSoft Mysore Meetup #47Mule event processing models | MuleSoft Mysore Meetup #47
Mule event processing models | MuleSoft Mysore Meetup #47
MysoreMuleSoftMeetup
 
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdfIGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
Amin Marwan
 

Recently uploaded (20)

Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
 
Temple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation resultsTemple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation results
 
B. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdfB. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdf
 
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdfANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
 
Constructing Your Course Container for Effective Communication
Constructing Your Course Container for Effective CommunicationConstructing Your Course Container for Effective Communication
Constructing Your Course Container for Effective Communication
 
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
 
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
 
math operations ued in python and all used
math operations ued in python and all usedmath operations ued in python and all used
math operations ued in python and all used
 
How to deliver Powerpoint Presentations.pptx
How to deliver Powerpoint  Presentations.pptxHow to deliver Powerpoint  Presentations.pptx
How to deliver Powerpoint Presentations.pptx
 
Mule event processing models | MuleSoft Mysore Meetup #47
Mule event processing models | MuleSoft Mysore Meetup #47Mule event processing models | MuleSoft Mysore Meetup #47
Mule event processing models | MuleSoft Mysore Meetup #47
 
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdfIGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
 

Recall that the Fibonacci and Lucas sequences Fn and Ln are (0, 1, 1.pdf

  • 1. Recall that the Fibonacci and Lucas sequences Fn and Ln are (0, 1, 1, 2, . . . ) and (2, 1, 3, 4, . . . ), respectively. Given that x0 = x1 for the sequence xn in part (d), show that the ratio xn/(Fn + Ln) does not depend on n. where part (d) gives xn = xn?1 + xn?2 where n >= ?? 2. Solution Sequence in part (d) is given by (x0, x0, 2x0, 3x0, 5x0,8x0,....) = x0(1,1,2,3,5,8,....) Fn + Ln = (2,2,4,6,10,....) = 2(1,1,2,3,5,8,....) So clearly if we divide the nth term of xn and Fn+Ln then we get xn/(Fn+Ln) = x0/2 which does not depend on n