Question

Show that $\sum_{n=1}^\infty \frac{1}{(\log(n))^p}$ diverges

score 85 · Answer 1 · 2026-04-09 02:43:47

85

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Show that $\sum_{n=1}^\infty \frac{1}{(\log(n))^p}$ diverges

Published on 09 Apr 2026 - 2:43

score 94 · Answer 2 · 2026-03-24 23:58:03

94

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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 3 · 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 69 · Answer 4 · 2026-04-10 06:30:09

69

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Calculate limit of $(1 + x^2 + y^2)^\frac{1}{x^2 + y^2 + xy^2}$ as $(x,y) \rightarrow (0,0)$

Published on 10 Apr 2026 - 6:30

score 264 · Answer 5 · 2026-04-09 03:15:20

264

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Calculate the sum of the series: $\sum\limits_{n=1}^{\infty}\left ( \frac{3}{n^{2}+n}-\frac{2}{4n^{2}+16n+15} \right )$

Published on 09 Apr 2026 - 3:15

score 109 · Answer 6 · 2026-04-09 00:10:13

109

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What happens to $\int_a^b \sin(\sqrt[n]{x})\,dx$ as $n\to\infty$?

Published on 09 Apr 2026 - 0:10

score 6k · Answer 7 · 2026-04-10 03:42:57

6k

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How do I prove that the limit as x approaches 0 of (sin(x)/x) = 1 using the definition of a limit?

Published on 10 Apr 2026 - 3:42

score 101 · Answer 8 · 2018-01-18 21:51:28

101

Views

Evaluate $\lim_{n\to \infty} \dfrac{\ln(n)^n}{5n^n}$

Published on 18 Jan 2018 - 21:51

score 65 · Answer 9 · 2018-01-18 22:07:41

65

Views

Use Taylor's theorem to evaluate the limit

Published on 18 Jan 2018 - 22:07

score 834 · Answer 10 · 2026-03-24 23:56:15

834

Views

Understanding a proof that if $|x|<1$ then $x^n \to 0$

Published on 24 Mar 2026 - 23:56

score 106 · Answer 11 · 2018-01-19 02:58:28

106

Views

Shall I change order of integral and limit

Published on 19 Jan 2018 - 2:58

score 80 · Answer 12 · 2018-01-19 08:40:45

80

Views

Evaluate: $\lim_{x\to 1} \dfrac {m}{x^m -1} - \dfrac {p}{x^p-1}$

Published on 19 Jan 2018 - 8:40

score 125 · Answer 13 · 2026-03-31 05:05:28

125

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How to evaluate $\lim_{x\rightarrow 0^-} \sec^{-1}(1+x)$?

Published on 31 Mar 2026 - 5:05

score 47 · Answer 14 · 2026-04-08 22:24:43

47

Views

Inferior limit when t decreases to 0

Published on 08 Apr 2026 - 22:24

score 1.3k · Answer 15 · 2026-04-09 05:33:24

1.3k

Views

How to prove this Dirac delta limit representation is correct?

Published on 09 Apr 2026 - 5:33

List Question

Show that $\sum_{n=1}^\infty \frac{1}{(\log(n))^p}$ diverges

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

Calculate limit of $(1 + x^2 + y^2)^\frac{1}{x^2 + y^2 + xy^2}$ as $(x,y) \rightarrow (0,0)$

Calculate the sum of the series: $\sum\limits_{n=1}^{\infty}\left ( \frac{3}{n^{2}+n}-\frac{2}{4n^{2}+16n+15} \right )$

What happens to $\int_a^b \sin(\sqrt[n]{x})\,dx$ as $n\to\infty$?

How do I prove that the limit as x approaches 0 of (sin(x)/x) = 1 using the definition of a limit?

Evaluate $\lim_{n\to \infty} \dfrac{\ln(n)^n}{5n^n}$

Use Taylor's theorem to evaluate the limit

Understanding a proof that if $|x|<1$ then $x^n \to 0$

Shall I change order of integral and limit

Evaluate: $\lim_{x\to 1} \dfrac {m}{x^m -1} - \dfrac {p}{x^p-1}$

How to evaluate $\lim_{x\rightarrow 0^-} \sec^{-1}(1+x)$?

Inferior limit when t decreases to 0

How to prove this Dirac delta limit representation is correct?

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