1) The document discusses infinite sequences and series. It provides definitions and formulas for convergent and divergent infinite sequences and series.
2) Examples are given to determine whether specific infinite sequences and series converge or diverge. Summations are calculated for convergent series.
3) Readers are asked to work through practice problems from their mathematics textbook and discuss questions about the unit material with teachers.
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
In algebra, the synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than the long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.
References:
https://en.wikipedia.org/wiki/Polynomial_long_division
https://en.wikipedia.org/wiki/Synthetic_division
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
In algebra, the synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than the long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.
References:
https://en.wikipedia.org/wiki/Polynomial_long_division
https://en.wikipedia.org/wiki/Synthetic_division
MATHS SYMBOLS - OTHER OPERATIONS (1) - ABSOLUTE VALUE - ROUNDING to INTEGER - PLUS or MINUS - RECIPROCAL - RATIO - PROPORTIONS and FIRST PROPERTIES - BRACKETS - EQUALITY SIGN - APPROXIMATELY EQUAL - NOT EQUAL - LESS - MUCH LESS - LESS THAN or EQUAL TO - GREATER - MUCH GREATER THAN - GREATER THAN or EQUAL TO - PROPORTIONALITY - DEFINITION
MATHS SYMBOLS - OTHER OPERATIONS (1) - ABSOLUTE VALUE - ROUNDING to INTEGER - PLUS or MINUS - RECIPROCAL - RATIO - PROPORTIONS and FIRST PROPERTIES - BRACKETS - EQUALITY SIGN - APPROXIMATELY EQUAL - NOT EQUAL - LESS - MUCH LESS - LESS THAN or EQUAL TO - GREATER - MUCH GREATER THAN - GREATER THAN or EQUAL TO - PROPORTIONALITY - DEFINITION
Questions of quantitative aptitude tests for competitive examinations Dr. Trilok Kumar Jain
This material is for PGPSE / CSE students of AFTERSCHOOOL. PGPSE / CSE are free online programme - open for all - free for all - to promote entrepreneurship and social entrepreneurship PGPSE is for those who want to transform the world. It is different from MBA, BBA, CFA, CA,CS,ICWA and other traditional programmes. It is based on self certification and based on self learning and guidance by mentors. It is for those who want to be entrepreneurs and social changers. Let us work together. Our basic idea is that KNOWLEDGE IS FREE & AND SHARE IT WITH THE WORLD
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
A Strategic Approach: GenAI in EducationPeter Windle
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.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2. Diskusikan dengan teman Anda mengenai konsep
deret dan barisan. Anda dapat mencarinya dari buku
atau dengan menggunakan internet. Kemudian,
Anda bisa menuliskan bentuk umum dari kedua
konsep tersebut dan tuliskan di dalam buku Anda.
Laporkan hasil pengerjaan Anda kepada guru.
Diskusi
3. Pernahkah Anda menyaksikan barisan semut berjalan? Dengan
kuasa-Nya, Tuhan telah menciptakan semut sedemikian rupa
sehingga mampu berjalan bersama koloninya dalam barisan yang
tersusun rapi.
4. Barisan tak hingga dinotasikan :
𝑎𝑛 𝑛=1
∞
Suatu barisan tak hingga dikatakan konvergen menuju 𝐿, Jika
lim
𝑛→∞
𝑎𝑛 = 𝐿
Definisi Konvergen Barisan Tak Hingga
5. Tentukan kekonvergenan dari barisan
𝑛3
𝑛2+𝑛 𝑛=1
∞
Penyelesaian
lim
𝑛→∞
𝑛3
𝑛2 + 𝑛
= lim
𝑛→∞
𝑛3
𝑛3
𝑛2 + 𝑛
𝑛3
= lim
𝑛→∞
𝑛2
𝑛 + 1
= ∞
𝑛3
𝑛2+𝑛 𝑛=1
∞
tidak konvergen atau disebut divergen.
Kesuksesan itu ditentukan oleh diri
sendiri, dan diri sendirilah yang
menentukan tolak ukur kesuksesan.
Maka tentukanlah kesuksesan seperti
apa yang ingin diraih.
Bangkit Karakter
6. 1. Tunjukkan bahwa deret geometri
2 5 5
+ 2 5 4
+ 2 5 3
+ 2 5 2
+ ⋯
konvergen.
2. Tunjukkan bahwa 1 −
1
𝑛
adalah
konvergen.
3. Tentukan apakah barisan 𝑎𝑛 =
3𝑛2−4
𝑛+2
konvergen atau divergen.
Kerjakan
Uji Materi 4.1 halaman 76
no 1-6, buku Matematika
untuk Kelas XI SMA
Kelompok Wajib.
7. Untuk −1 < 𝑟 < 1, maka
𝑆∞ = 𝑈1 + 𝑈2 + 𝑈3 + ⋯
Disebut deret geometri tak hingga konvergen yang
memiliki limit jumlah
𝑆𝑛 =
𝑈1
1 − 𝑟
Untuk 𝑟 < −1 atau 𝑟 > 1, deretnya adalah deret
divergen yang tidak mempunyai limit jumlah.
Rumus Jumlah Deret Tak Hingga Konvergen
Buktikan bahwa 𝑆𝑛 =
𝑈1
1−𝑟
untuk deret geometri tak
hingga konvergen.
10. sebuah bola pimpong dijatuhkan ke lantai dari ketinggian 2 meter.
Setiap kali setelah bola itu memantul ia mencapai ketinggian tiga per
empat dari ketinggian yang dicapai sebelumnya. Panjang lintasan bola
tersebut dari pantulan ke tiga sampai ia berhenti adalah …
𝑈1 = 2
𝑈2 =
6
4
𝑈3 =
18
16
𝑈4 =
27
32
𝑆∞ =
𝑈4
1 − 𝑟
=
27
32
1 −
3
4
=
27
32
1
4
=
27
8
= 3,38 𝑚𝑒𝑡𝑒𝑟
Jadi, panjang lintasan 3,38 meter.
11. 1. jumlah semua suku deret geometri
tak berhingga adalah 9, sedangkan
jumlah suku yang bernomor genap
adalah
9
4
. Maka suku pertama deret
tersebut adalah …
2. Nyatakan desimal berulang
0,125125125 … dalam penjumlahan
pecahan, dan tentukan hasil
penjumlahannya tersebut.
3. −1 +
2
3
−
3
5
+
4
7
−
5
9
= ⋯
Kerjakan
Uji Materi 4.1 halaman 76
tingkat 2, buku
Matematika untuk Kelas XI
SMA Kelompok Wajib.
13. Kuis
Kerjakan
Uji Kompetensi Unit 4
halaman 77-78, buku
Matematika untuk Kelas XI
SMA Kelompok Wajib.
1. Periksalah deret berikut konvergen atau divergen, jika
konvergen tentukan jumlahnya.
𝑘=1
∞
1
𝑘
−
1
𝑘 + 1
2. Sebuah bola dijatuhkan dari ketinggian 100 kaki. Tiap
kali bola tersebut mengenai lantai, ia pantulkan setinggi
2
3
dari tinggi sebelumnya. Tentukan jarak seluruhnya yang
ditempuh bola tersebut.
14. “Anda berhasil saat Anda mulai
bergerak menuju langkah
kebaikan”
Charles Cartson
