Question

Find the partial sum formula of $\sum_{i=1}^n \frac{x^{2^{i-1}}}{1-x^{2^i}}$

score 118 · Answer 1 · 2019-04-15 08:51:37

118

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Find the partial sum formula of $\sum_{i=1}^n \frac{x^{2^{i-1}}}{1-x^{2^i}}$

Published on 15 Apr 2019 - 8:51

score 85 · Answer 2 · 2026-03-29 23:59:45

85

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What is $\sum_{k=1}^m\left[2^k\begin{pmatrix} n \\ k \end{pmatrix}\right]^2$?

Published on 29 Mar 2026 - 23:59

score 1.9k · Answer 3 · 2026-04-02 12:32:52

1.9k

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Derive the sum of $\sum_{i=1}^n ix^{i-1}$

Published on 02 Apr 2026 - 12:32

score 8.6k · Answer 4 · 2026-04-01 12:51:15

8.6k

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Find the Sum of the Series: $\sum_{0}^{\infty}\frac{(-1)^n\pi^{2n}}{6^{2n}(2n)!}$

Published on 01 Apr 2026 - 12:51

score 21 · Answer 5 · 2019-04-15 16:34:01

21

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Proving $\sum_{j=0}^{N-1}\cos\frac{\left(2j+1\right)\pi}{2N}=0$

Published on 15 Apr 2019 - 16:34

score 107 · Answer 6 · 2019-04-15 18:47:56

107

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Find the infinite sum $\sum^\infty_{n=2}\frac{\left(-1\right)^{n}}{\log n}$, speed up its convergence

Published on 15 Apr 2019 - 18:47

score 98 · Answer 7 · 2026-02-23 00:51:10

98

Views

Rewriting a set of integers to get rid of repetition but keeping subset sum ordering

Published on 23 Feb 2026 - 0:51

score 399 · Answer 8 · 2026-03-26 12:40:48

399

Views

Infinite sums and squares

Published on 26 Mar 2026 - 12:40

score 1k · Answer 9 · 2026-04-03 02:19:27

1k

Views

Separating out the last term of a given sequence

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score 104 · Answer 10 · 2019-04-16 16:50:51

104

Views

$\sum_{n=1}^\infty \frac{n}{4n^4+1}$ converges to?

Published on 16 Apr 2019 - 16:50

score 52 · Answer 11 · 2026-03-27 15:35:55

52

Views

Algorithm Complexity - Summation - Correctly interpreted how to do it.

Published on 27 Mar 2026 - 15:35

score 715 · Answer 12 · 2026-03-26 06:31:44

715

Views

What is the value of $\frac11+\frac13-\frac15-\frac17+\frac19+\frac1{11}-\dots$?

Published on 26 Mar 2026 - 6:31

score 104 · Answer 13 · 2026-03-26 17:35:06

104

Views

Sum of alternating binomial-coefficient-type series

Published on 26 Mar 2026 - 17:35

score 1.7k · Answer 14 · 2019-04-17 16:10:16

1.7k

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Find $\lim_{t\to 1^{-}}(1-t)\sum_{r = 1}^\infty \frac{t^r}{t^r+1}$

Published on 17 Apr 2019 - 16:10

score 391 · Answer 15 · 2026-03-26 17:31:21

391

Views

Closed form of recurrent arithmetic series summation

Published on 26 Mar 2026 - 17:31

List Question

Find the partial sum formula of $\sum_{i=1}^n \frac{x^{2^{i-1}}}{1-x^{2^i}}$

What is $\sum_{k=1}^m\left[2^k\begin{pmatrix} n \\ k \end{pmatrix}\right]^2$?

Derive the sum of $\sum_{i=1}^n ix^{i-1}$

Find the Sum of the Series: $\sum_{0}^{\infty}\frac{(-1)^n\pi^{2n}}{6^{2n}(2n)!}$

Proving $\sum_{j=0}^{N-1}\cos\frac{\left(2j+1\right)\pi}{2N}=0$

Find the infinite sum $\sum^\infty_{n=2}\frac{\left(-1\right)^{n}}{\log n}$, speed up its convergence

Rewriting a set of integers to get rid of repetition but keeping subset sum ordering

Infinite sums and squares

Separating out the last term of a given sequence

$\sum_{n=1}^\infty \frac{n}{4n^4+1}$ converges to?

Algorithm Complexity - Summation - Correctly interpreted how to do it.

What is the value of $\frac11+\frac13-\frac15-\frac17+\frac19+\frac1{11}-\dots$?

Sum of alternating binomial-coefficient-type series

Find $\lim_{t\to 1^{-}}(1-t)\sum_{r = 1}^\infty \frac{t^r}{t^r+1}$

Closed form of recurrent arithmetic series summation

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