Question

Prove that $1 + \frac{2}{3!} + \frac{3}{5!} + \frac{4}{7!} + \dotsb = \frac{e}{2}$

score 539 · Answer 1 · 2026-04-17 14:34:46

539

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Prove that $1 + \frac{2}{3!} + \frac{3}{5!} + \frac{4}{7!} + \dotsb = \frac{e}{2}$

Published on 17 Apr 2026 - 14:34

score 190 · Answer 2 · 2026-04-11 21:00:37

190

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Summing a series having a geometric component

Published on 11 Apr 2026 - 21:00

score 97 · Answer 3 · 2026-04-16 12:43:38

97

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How can we use sequence $x_{n+1}=3-\frac{1}{x_n}$ , when $x_1=1 $ to evaluate $\sqrt5$?

Published on 16 Apr 2026 - 12:43

score 1.2k · Answer 4 · 2026-04-16 05:55:31

1.2k

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Convergent sequence in Hilbert space

Published on 16 Apr 2026 - 5:55

score 1.8k · Answer 5 · 2026-04-14 03:32:11

1.8k

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How to prove the series $\sum\limits_{n=1}^\infty\frac1n\sin(\ln n)$ diverges

Published on 14 Apr 2026 - 3:32

score 122 · Answer 6 · 2026-05-10 16:11:13

122

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Concrete Mathematics chapter 2 infinite calculus (geometric series)

Published on 10 May 2026 - 16:11

score 109 · Answer 7 · 2026-05-11 00:31:05

109

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Why am I getting no order of magnitude for the error in a Newton-Raphson method problem?

Published on 11 May 2026 - 0:31

score 115 · Answer 8 · 2026-04-16 12:52:21

115

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On the sum of Double Power Series $\sum\limits_{-\infty}^{+\infty}\space\frac{2^n}{{x}^{2^n}+1}$

Published on 16 Apr 2026 - 12:52

score 335 · Answer 9 · 2026-04-16 19:17:09

335

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Given this operation $\phi$ on natural number sequences, show $\phi^3=\phi$.

Published on 16 Apr 2026 - 19:17

score 1.2k · Answer 10 · 2026-04-10 17:42:58

1.2k

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Why does this series have a different sum when its terms are rearranged?

Published on 10 Apr 2026 - 17:42

score 441 · Answer 11 · 2026-05-10 15:10:27

441

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An Euler type sum: $\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n\cdot 4^n}{2n \choose n}$, where $H_n^{(2)}=\sum\limits_{k=1}^{n}\frac{1}{k^2}$

Published on 10 May 2026 - 15:10

score 87 · Answer 12 · 2026-04-16 09:34:59

87

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Show that $ \lim_{j\to\infty}\prod_{n=j}^{mj}\frac{\pi}{2\tan^{-1}(kn)}=m^{\frac{2}{k\pi}}$

Published on 16 Apr 2026 - 9:34

score 110 · Answer 13 · 2026-04-15 04:11:26

110

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Example of series such that every $\sum_{i=1}^{\infty} b_{n_i}$ converges but $\sum_{n=1}^{\infty} |b_n|$ diverges

Published on 15 Apr 2026 - 4:11

score 164 · Answer 14 · 2026-04-16 07:26:17

164

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Proofs for series forms of $\operatorname{Si}(x)$, $\operatorname{Ci}(x)$ and $\operatorname{Li}(x)$

Published on 16 Apr 2026 - 7:26

score 996 · Answer 15 · 2026-04-11 12:15:59

996

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How do I convert a sum (from $1$ to $n$) of powers into a function of $n$?

Published on 11 Apr 2026 - 12:15

List Question

Prove that $1 + \frac{2}{3!} + \frac{3}{5!} + \frac{4}{7!} + \dotsb = \frac{e}{2}$

Summing a series having a geometric component

How can we use sequence $x_{n+1}=3-\frac{1}{x_n}$ , when $x_1=1 $ to evaluate $\sqrt5$?

Convergent sequence in Hilbert space

How to prove the series $\sum\limits_{n=1}^\infty\frac1n\sin(\ln n)$ diverges

Concrete Mathematics chapter 2 infinite calculus (geometric series)

Why am I getting no order of magnitude for the error in a Newton-Raphson method problem?

On the sum of Double Power Series $\sum\limits_{-\infty}^{+\infty}\space\frac{2^n}{{x}^{2^n}+1}$

Given this operation $\phi$ on natural number sequences, show $\phi^3=\phi$.

Why does this series have a different sum when its terms are rearranged?

An Euler type sum: $\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n\cdot 4^n}{2n \choose n}$, where $H_n^{(2)}=\sum\limits_{k=1}^{n}\frac{1}{k^2}$

Show that $ \lim_{j\to\infty}\prod_{n=j}^{mj}\frac{\pi}{2\tan^{-1}(kn)}=m^{\frac{2}{k\pi}}$

Example of series such that every $\sum_{i=1}^{\infty} b_{n_i}$ converges but $\sum_{n=1}^{\infty} |b_n|$ diverges

Proofs for series forms of $\operatorname{Si}(x)$, $\operatorname{Ci}(x)$ and $\operatorname{Li}(x)$

How do I convert a sum (from $1$ to $n$) of powers into a function of $n$?

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