Part 1 sequence and arithmetic progressionSatish Pandit
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In this presentation, you will learn sequences and arithmetic progression. How to find the terms, common differences, etc. I have given detailed solutions to each problem.
Part 1 sequence and arithmetic progressionSatish Pandit
Β
In this presentation, you will learn sequences and arithmetic progression. How to find the terms, common differences, etc. I have given detailed solutions to each problem.
You will learn how to derive patterns in series, also expressing it into summation notation.
For more instructional resources, CLICK me here! πππ
https://tinyurl.com/y9muob6q
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https://tinyurl.com/ycjp8r7u
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You will learn how to derive patterns in series, also expressing it into summation notation.
For more instructional resources, CLICK me here! πππ
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! πππ
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
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Francesca Gottschalk from the OECDβs Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Operation βBlue Starβ is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
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Letβs explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
A Strategic Approach: GenAI in EducationPeter Windle
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. What is a SEQUENCE?
ο In mathematics, a sequence is an ordered list.
Like a set, it contains members (also
called elements, or terms). The number of
ordered elements (possibly infinite) is called
the length of the sequence. Unlike a set, order
matters, and exactly the same elements can
appear multiple times at different positions in
the sequence. Most precisely, a sequence
can be defined as a function whose domain
is a countable totally ordered set, such as
the natural numbers.
Source:
Wikipedia:http://en.wikipedia.org/wiki/Sequence
3. INFINITE SEQUENCE
ο An infinite sequence is a function with domain the set of
natural numbers π = 1, 2, 3, β¦ β¦ β¦ .
ο For example, consider the function "πβ defined by
π π = π2 π = 1, 2, 3, β¦ β¦
Instead of the usual functional notation π π , for
sequences we usually write
ππ = π2
That is, a letter with a subscript, such as ππ, is used to
represent numbers in the range of a sequence. For the
sequence defined by ππ = π2,
π1 = 12
= 1
π2 = 22
= 4
π3 = 32
= 9
π4 = 42
= 16
4. General or nth Term
ο A sequence is frequently defined by giving its
range. The sequence on the given example
can be written as
1, 4, 9, 16, β¦ β¦ β¦ , π2
, β¦ β¦
Each number in the range of a sequence
is a term of the sequence, with ππ the nth term
or general term of the sequence. The formula
for the nth term generates the terms of a
sequence by repeated substitution of counting
numbers for π.
5. FINITE SEQUENCE
ο A finite sequence with π terms is a
function with domain the set of natural
numbers 1, 2,3, β¦ β¦ , π
ο For example, 2, 4, 6, 8, 10 is a finite
sequence with 5 terms where ππ = 2π, for
π = 1,2,3,4,5. In contrast, 2,4,6,8,10, β¦ β¦ is an
infinite sequence where ππ = 2π, for π =
1,2,3,4,5 β¦ β¦.
6. Sample Problems
1. Write the first five terms of the infinite sequence
with general term ππ = 2π β 1.
Answer:
π1 = 2 1 β 1 = 1
π2 = 2 2 β 1 = 3
π3 = 2 3 β 1 = 5
π4 = 2 4 β 1 = 7
π5 = 2 5 β 1 = 9
Thus, the first five terms are 1,3,5,7,9 and the
sequence is
1, 3, 5, 7, 9, β¦ β¦ 2π β 1, β¦ β¦
7. 2. A finite sequence has four terms, and the formula for the
nth term is π₯π = β1 π 1
2πβ1. What is the sequence?
Answer:
π₯1 = β1 1 1
21β1 = β1
π₯2 = β1 2 1
22β1 =
1
2
π₯3 = β1 3 1
23β1 = β
1
4
π₯4 = β1 4 1
24β1 =
1
8
Thus the sequence is
β1,
1
2
, β
1
4
,
1
8
8. 3. Find a formula for ππ given the first few terms
of the sequence.
a.) 2, 3, 4, 5, β¦
Answer: Each term is one larger than the
corresponding natural number. Thus, we have,
π1 = 2 = 1 + 1
π2 = 3 = 2 + 1
π3 = 4 = 3 + 1
π4 = 5 = 4 + 1
Hence, ππ = π + 1
10. SERIES
ο Associated with every sequence, is a
SERIES, the indicated sum of the
sequence.
ο For example, associated with the
sequence 2, 4, 6, 8, 10, is the series
2+4+6+8+10 and associated with the
sequence -1, Β½, -1/4, 1/8, is the series
(-1)+(1/2)+(-1/4)+(1/8).
11. Sigma Summation Notation
ο The Greek letter β (sigma) is often used as a
summation symbol to abbreviate a series.
ο The series 2 + 4 +6 + 8 + 10 which has a general
term π₯π = 2π, can be written as
π=1
5
π₯π ππ
π=1
5
2π
and is read as βthe sum of the terms π₯π or 2π as π
varies from 1 to 5β. The letter π is the index on the
summation while 1 and 5 are the lower and upper
limits of summation, respectively.
12. ο In general, if π₯1, π₯2, π₯3, π₯4 β¦ , π₯π is a
sequence associated with a series of
π=1
π
π₯π = π₯1 + π₯2 + π₯3 + π₯4 + β― + π₯π
15. Break a leg!
1. Find the first four terms and the seventh
term π = 1,2,3, 4 &7 if the general term
of the sequence is π₯π =
β1 π
π
.
2. Find a formula for ππ given the few terms
of the sequence.
1
2
,
1
4
,
1
8
,
1
16
, β¦