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- Notes of Fourier Series
- Some important series of functions
- Chapter 08: Infinite Series
- Ch 06: Sequences and Series
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- Chapter 08: Infinite Series @bsc:notes_of_mathematical_method
- ====== Chapter 08: Infinite Series ====== <HTML><img src="http://mathcity.org/images/series.gif" title="Geometric series" class="mediaright" alt="Geometric series" /></HTML> Notes of the book Mathematical Method written by S.M
- Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
- rges to the same limit.</collapse> </panel> ==== Series of Numbers ==== <panel> 1. A series $\sum_{n=1}^\infty a_n$ is said to be convergent if the sequence $\{... wer</btn><collapse id="301" collapsed="true">(B): Series is convergent if its sequence of partial sume is ... divergent test</collapse> </panel> <panel> 4. A series $\sum_{n=1}^\infty \left( 1+\frac{1}{n} \right)$
- Question 1 Exercise 5.1 @math-11-kpk:sol:unit05
- stion 1 of Exercise 5.1 of Unit 05: Mascellaneous series. This is unit of A Textbook of Mathematics for Gr... hawar, Pakistan. =====Question 1(i)===== Sum the series $1^2+3^2+5^2+7^2+\ldots$ up to $n$ terms. ====Solution==== We see that each term of the given series is square of the terms of the series $1+3+5+\ldots$ whose $n^{\text {th }}$ term is $2 n-1$. Therefore
- FSc Part 1 (KPK Boards) @fsc
- quence. * define arithmetic mean and arithmetic series. * solve real life problems involving arithmetic series. * define a geometric sequence. * solve probl... equences. * define geometric mean and geometric series. * solve real life problems involving geometric series. * recognize a harmonic sequence and find its n
- Question 1 Exercise 5.3 @math-11-kpk:sol:unit05
- stion 1 of Exercise 5.4 of Unit 05: Mascellaneous series. This is unit of A Textbook of Mathematics for Gr... istan. =====Question 1(i)==== Find the sum of the series $\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\ld... $ terms. ====Solution==== The general term of the series is: $$T_n=\dfrac{1}{n(n+1)}$$ Resolving $T_n$ int... =\dfrac{n}{n+1} \end{align} Hence the sum of the series is: $$S_n=\dfrac{n}{n+1}$$ =====Question 1(ii)==
- Question 7 Review Exercise @math-11-kpk:sol:unit05
- on 7 of Review Exercise of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... tan. =====Question 7(i)===== Find the sum of the series: $1.2^2+3.3^2+5.4^2+\ldots$ to $n$ terms. ====Solution==== The given series if the product of corresponding terms of the two series $1,3,5, \ldots,(2 n-1)$ and $2^2, 3^2, 4^2, \ldot
- MTH322: Real Analysis II (Fall 2021) @atiq
- uity, differentiation, integration, sequences and series of numbers, that is many notion included in [[ati... rithmic function, the trigonometric functions. **Series of functions:** Absolute convergence, uniform con... gence, Cauchy criterion, Weiestrass M-test, power series of functions, radius of convergence, Cauchy-Hadam... nline_view|View Online]] * Review: Sequences & Series | {{ :atiq:fa21-mth322-pre-ch02.pdf |Download PDF
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university
- s-II or Mathematical Methods: (Geometry, Infinite Series, Complex Numbers, Linear Algebra, Differential Eq... ==== ===Mathematical Methods: (Geometry, Infinite Series, Complex Numbers, Linear Algebra, Differential Eq... , logarithmic, hyperbolic, exponential functions; Series solution by using complex numbers Sequence and Series: Sequences, Infinite series: Convergence of sequen
- Question 2 & 3 Exercise 5.1 @math-11-kpk:sol:unit05
- n 2 & 3 of Exercise 5.1 of Unit 05: Miscullaneous Series. This is unit of A Textbook of Mathematics for Gr... $1.2+2.3+3.4+\ldots+99.100$. Solution: The given series is the product of the corresponding terms of the series $1+2+3+\ldots+99$ and $2+3+4+\ldots+100$, whose $... n^{\text {th }}$ terms are $n(n+1)$ and the given series have 99 terms. Therefore, the $n^{\text {th }}$ t
- Question 10 Exercise 7.3 @math-11-kpk:sol:unit07
- war, Pakistan. Q10 Find the sum of the following series: (i) $1-\frac{1}{2^2}+\frac{1.3}{2 !} \cdot \frac{1}{2^4}+\ldots$ Solution: The given series is binomial series. Let it be identical with the expansion of $(1+x)^n$ that is $$ \begin{aligned} & 1+n ... } x^3+\ldots \end{aligned} $$ Comparing both the series, we have $n x=-\frac{1}{4}$ (I) and $\frac{n(n-1)
- MTH322: Real Analysis II (Spring 2023) @atiq
- uity, differentiation, integration, sequences and series of numbers, that is many notions included in [[at... rithmic function, the trigonometric functions. **Series of functions:** Absolute convergence, uniform con... gence, Cauchy criterion, Weiestrass M-test, power series of functions, radius of convergence, Cauchy-Hadam... if and only if $M_n\to 0$ as $n\to \infty$. - A series of functions $\sum f_n$ will converge uniformly (
- Notes of Fourier Series @bsc
- ====== Notes of Fourier Series====== These notes are provided by Mr. Muhammad Ashfaq. We are really very... ry periods * Even and odd functions * Fourier series for even and odd functions * Half range fourier series * Fourier cosine series ==== View online ==== {{gview noreference>:bsc:notes-fourier-series.pdf}} ===
- Real Analysis Notes by Prof Syed Gul Shah @notes
- : Real Number system * Chapter 02: Sequence and Series * Sequence, Subsequence, Increasing Sequenc... to\infty}\left(\sup {s_n}\right)$. * Infinite Series. * Theorem: If $\sum_{n=1}^\infty{a_n}$ conv... * Theorem (General Principle of Convergence): A series $\sum{a_n}$ is convergent if and only if for any ... $. * Theorem: Let $\sum {a_n}$ be an infinite series of non-negative terms and let $\{s_n\}$ be a sequ
- Unit 04: Sequence and Series (Solutions) @math-11-kpk:sol
- ===== Unit 04: Sequence and Series (Solutions) ===== This is a forth unit of the book Mathematics 11 publ... ans tEtween two numtErs. * Define an arithmetic series. * Establish the formula to find the sum to n terms of an arithmetic series. * Show that sum of $n$ arithmetic means betwee... * Solve real life problems involving arithmetic series. * Define a geometric sequence. * Find the $n
- Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
- ====== Chapter 02 - Sequence and Series ====== ==== Contents ==== * Sequence, Subsequence, Increasing... n\to\infty}\left(\sup {s_n}\right)$. * Infinite Series. * Theorem: If $\sum_{n=1}^\infty{a_n}$ conver... * Theorem (General Principle of Convergence): A series $\sum{a_n}$ is convergent if and only if for any ... _0$. * Theorem: Let $\sum {a_n}$ be an infinite series of non-negative terms and let $\{s_n\}$ be a sequ