Question

A constant and divergent series

score 1.5k · Answer 1 · 2026-04-01 08:12:52

1.5k

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A constant and divergent series

Published on 01 Apr 2026 - 8:12

score 162 · Answer 2 · 2018-01-17 20:24:39

162

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STEP paper 1 1999 question - is it possible to justify this solution?

Published on 17 Jan 2018 - 20:24

score 258 · Answer 3 · 2026-04-09 00:04:29

258

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transforming sigma notation into harmonic series. CLRS A.1-2

Published on 09 Apr 2026 - 0:04

score 1.8k · Answer 4 · 2018-01-18 02:40:30

1.8k

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Sum of series $\frac {4}{10}+\frac {4\cdot7}{10\cdot20}+ \frac {4\cdot7\cdot10}{10\cdot20\cdot30}+\cdots$

Published on 18 Jan 2018 - 2:40

score 72 · Answer 5 · 2026-04-06 00:50:37

72

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How to prove $\lim \limits_{\alpha\rightarrow \infty} (\sum_{n=1}^{\infty}[(a_{n}+\frac{1}{(1+n)^{\alpha}})^{n}-{a}_{n}^{n}]) = 0 $

Published on 06 Apr 2026 - 0:50

score 38 · Answer 6 · 2026-04-05 08:37:53

38

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Consider this limit

Published on 05 Apr 2026 - 8:37

score 1.4k · Answer 7 · 2026-03-24 23:58:04

1.4k

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If $f(x)=\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)!!}$ then prove that $f'(x)=1+xf(x)$

Published on 24 Mar 2026 - 23:58

score 52 · Answer 8 · 2026-04-10 01:31:54

52

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Recurrence relation of the series

Published on 10 Apr 2026 - 1:31

score 39 · Answer 9 · 2026-04-09 13:27:08

39

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Prove that the given series of functions is continuously differentiable.

Published on 09 Apr 2026 - 13:27

score 106 · Answer 10 · 2026-04-01 17:03:26

106

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Convergence/divergence of these series

Published on 01 Apr 2026 - 17:03

score 94 · Answer 11 · 2026-03-24 23:58:03

94

Views

If $f\left(x\right)=$ $\sum_{n=0}^{\infty}$ $\frac{x^{3n}}{\left(3n\right)!}$ then prove $f''\left(x\right)+f'\left(x\right)+f\left(x\right)=e^{x}$

Published on 24 Mar 2026 - 23:58

score 94 · Answer 12 · 2026-03-24 23:56:02

94

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Convergence of the series $\sum\limits_{n=1}^\infty n\sin(2^{-n})$

Published on 24 Mar 2026 - 23:56

score 383 · Answer 13 · 2026-04-09 00:54:23

383

Views

Ratio of terms in simple geometric sequence appears inconsistent?

Published on 09 Apr 2026 - 0:54

score 50 · Answer 14 · 2026-03-24 23:44:28

50

Views

Prove that $\{a_n\}$ is a monotonically increasing sequence and it bounded by $c$.

Published on 24 Mar 2026 - 23:44

score 104 · Answer 15 · 2026-04-09 19:36:55

104

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Calculate expected value based on geometric series

Published on 09 Apr 2026 - 19:36

List Question

A constant and divergent series

STEP paper 1 1999 question - is it possible to justify this solution?

transforming sigma notation into harmonic series. CLRS A.1-2

Sum of series $\frac {4}{10}+\frac {4\cdot7}{10\cdot20}+ \frac {4\cdot7\cdot10}{10\cdot20\cdot30}+\cdots$

How to prove $\lim \limits_{\alpha\rightarrow \infty} (\sum_{n=1}^{\infty}[(a_{n}+\frac{1}{(1+n)^{\alpha}})^{n}-{a}_{n}^{n}]) = 0 $

Consider this limit

If $f(x)=\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)!!}$ then prove that $f'(x)=1+xf(x)$

Recurrence relation of the series

Prove that the given series of functions is continuously differentiable.

Convergence/divergence of these series

If $f\left(x\right)=$ $\sum_{n=0}^{\infty}$ $\frac{x^{3n}}{\left(3n\right)!}$ then prove $f''\left(x\right)+f'\left(x\right)+f\left(x\right)=e^{x}$

Convergence of the series $\sum\limits_{n=1}^\infty n\sin(2^{-n})$

Ratio of terms in simple geometric sequence appears inconsistent?

Prove that $\{a_n\}$ is a monotonically increasing sequence and it bounded by $c$.

Calculate expected value based on geometric series

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