Question

If $g(x)=\sum_{n=1}^{\infty}\frac{x^n}{n(n+1)}$, then prove that $\lim\limits_{x\to 1^{-}}g(x)$ exists and find this limit

score 121 · Answer 1 · 2026-04-16 17:49:25

121

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If $g(x)=\sum_{n=1}^{\infty}\frac{x^n}{n(n+1)}$, then prove that $\lim\limits_{x\to 1^{-}}g(x)$ exists and find this limit

Published on 16 Apr 2026 - 17:49

score 54 · Answer 2 · 2026-04-11 00:12:54

54

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Why is my method of finding $A_7$ wrong?

Published on 11 Apr 2026 - 0:12

score 48 · Answer 3 · 2026-04-13 16:04:56

48

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Can we plug a linear sequence of real numbers into the sine function such that the resulting sequence will be a one-to-one sequence?

Published on 13 Apr 2026 - 16:04

score 51 · Answer 4 · 2026-04-16 08:20:15

51

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Expanding $\left(\sum_{r=1, r\neq i}^mT_r\right)\left(\sum_{s=1, s\neq i}^mT_s^{-1}\right).$

Published on 16 Apr 2026 - 8:20

score 810 · Answer 5 · 2026-04-17 15:14:33

810

Views

Find the interval of convergence of the following series $\sum_{n=1}^{\infty}\frac{n^n x^n}{n!}$

Published on 17 Apr 2026 - 15:14

score 74 · Answer 6 · 2026-04-15 22:07:54

74

Views

Name of the following summation: $\sum_{a=b}^{\infty}{\binom{a-1}{b-1}x^{a-b}}=(1-x)^{-b}$

Published on 15 Apr 2026 - 22:07

score 53 · Answer 7 · 2026-04-14 22:41:08

53

Views

infinite series containing cos(x/n)

Published on 14 Apr 2026 - 22:41

score 42 · Answer 8 · 2026-05-14 06:40:45

42

Views

Iterated Sums of Differences

Published on 14 May 2026 - 6:40

score 364 · Answer 9 · 2026-04-09 22:42:34

364

Views

Proof of the Squeeze theorem for Sequences

Published on 09 Apr 2026 - 22:42

score 60 · Answer 10 · 2026-05-11 05:28:35

60

Views

Recurrence Relations Defined In Terms of Each Other to Closed Form

Published on 11 May 2026 - 5:28

score 144 · Answer 11 · 2026-05-11 08:31:13

144

Views

How to prove this sequence converges to 1?

Published on 11 May 2026 - 8:31

score 336 · Answer 12 · 2026-05-10 20:40:39

336

Views

lim inf and lim sup of sequence obtained from combination of two sequences

Published on 10 May 2026 - 20:40

score 51 · Answer 13 · 2026-04-14 21:06:08

51

Views

How can I prove this sequence of functions pointwisely converges to zero using formal argument?

Published on 14 Apr 2026 - 21:06

score 91 · Answer 14 · 2026-04-16 17:31:48

91

Views

$\sum_\limits{n=1}^{\infty}\frac{nx}{(1+x)(1+2x)...(1+nx)}$ convergence domain.

Published on 16 Apr 2026 - 17:31

score 482 · Answer 15 · 2026-05-11 09:35:33

482

Views

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

Published on 11 May 2026 - 9:35

List Question

If $g(x)=\sum_{n=1}^{\infty}\frac{x^n}{n(n+1)}$, then prove that $\lim\limits_{x\to 1^{-}}g(x)$ exists and find this limit

Why is my method of finding $A_7$ wrong?

Can we plug a linear sequence of real numbers into the sine function such that the resulting sequence will be a one-to-one sequence?

Expanding $\left(\sum_{r=1, r\neq i}^mT_r\right)\left(\sum_{s=1, s\neq i}^mT_s^{-1}\right).$

Find the interval of convergence of the following series $\sum_{n=1}^{\infty}\frac{n^n x^n}{n!}$

Name of the following summation: $\sum_{a=b}^{\infty}{\binom{a-1}{b-1}x^{a-b}}=(1-x)^{-b}$

infinite series containing cos(x/n)

Iterated Sums of Differences

Proof of the Squeeze theorem for Sequences

Recurrence Relations Defined In Terms of Each Other to Closed Form

How to prove this sequence converges to 1?

lim inf and lim sup of sequence obtained from combination of two sequences

How can I prove this sequence of functions pointwisely converges to zero using formal argument?

$\sum_\limits{n=1}^{\infty}\frac{nx}{(1+x)(1+2x)...(1+nx)}$ convergence domain.

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

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