List questions from telescopic-series

Published on 25 Nov 2017 - 16:55

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Determine the convergence of $\sum\limits_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $

Published on 07 Dec 2017 - 19:54

99

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Closed form solution for the series $\sum _{n=1} ^{\infty} \frac{1}{2^n+1}$

Published on 10 Dec 2017 - 21:27

2.5k

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If $|x_{n+1} - x_n| < \epsilon,$ is $(x_n) $ a Cauchy sequence?

Published on 13 Dec 2017 - 16:41

78

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Evaluation of $\sum_{n=a}^\infty\frac1{2n(n+1)}$ and $\sum_{n=1}^\infty\frac1{2n^2-\frac12}$

Published on 20 Dec 2017 - 8:36

147

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How to find the sum of the series?

Published on 20 Dec 2017 - 17:41

922

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Series involving Fibonacci Numbers: $\sum_{k=1}^\infty \frac{1}{F_kF_{k+1}}$

Published on 25 Dec 2017 - 22:56

1.2k

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Find $\sum_{k=1}^\infty\frac{1} {k(k+1)(k+2)(k+3)}$

Published on 02 Jan 2018 - 18:21

150

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Some infinite series (just for fun!)

Published on 05 Jan 2018 - 0:22

3k

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find sum of n terms of the sequence 1.3.(2^2) + 2.4.(3^2)+3.5.(4^2)+.......

Published on 07 Jan 2018 - 5:57

17.8k

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How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$

Published on 21 Nov 2010 - 17:28

4k

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Prove $\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots$ converges to $\frac 1 2 $

Published on 31 Jul 2012 - 23:16

3.5k

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What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$

Published on 24 Jan 2013 - 18:17

122

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Evaluate $\sum_{r=1}^{m} \frac{(r-1)m^{r-1}}{r\cdot\binom{m}{r}}$

Published on 31 Jul 2020 - 14:09

48

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Why is $(n+1)^3 = \sum_{k=0}^n (k+1)^3 - k^3$?

Published on 19 Aug 2020 - 2:00

List Question

Telescoping Series - Summation korean problem

Determine the convergence of $\sum\limits_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $

Closed form solution for the series $\sum _{n=1} ^{\infty} \frac{1}{2^n+1}$

If $|x_{n+1} - x_n| < \epsilon,$ is $(x_n) $ a Cauchy sequence?

Evaluation of $\sum_{n=a}^\infty\frac1{2n(n+1)}$ and $\sum_{n=1}^\infty\frac1{2n^2-\frac12}$

How to find the sum of the series?

Series involving Fibonacci Numbers: $\sum_{k=1}^\infty \frac{1}{F_kF_{k+1}}$

Find $\sum_{k=1}^\infty\frac{1} {k(k+1)(k+2)(k+3)}$

Some infinite series (just for fun!)

find sum of n terms of the sequence 1.3.(2^2) + 2.4.(3^2)+3.5.(4^2)+.......

How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$

Prove $\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots$ converges to $\frac 1 2 $

What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$

Evaluate $\sum_{r=1}^{m} \frac{(r-1)m^{r-1}}{r\cdot\binom{m}{r}}$

Why is $(n+1)^3 = \sum_{k=0}^n (k+1)^3 - k^3$?

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