Question

Asymptotic behavior of the sequence $u_n=\int_0^1\frac{e^{-t}}{t+\frac{1}{n}}dt$

score 97 · Answer 1 · 2026-04-17 15:49:07

97

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Asymptotic behavior of the sequence $u_n=\int_0^1\frac{e^{-t}}{t+\frac{1}{n}}dt$

Published on 17 Apr 2026 - 15:49

score 58 · Answer 2 · 2026-04-24 20:34:03

58

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Calculate the limit of $\left(\frac{n+1}{n-5}\right)^{5n-2}$

Published on 24 Apr 2026 - 20:34

score 60 · Answer 3 · 2026-04-17 08:23:34

60

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$\sum_{n=0}^{\infty}(2+(-1)^n)x^n$ radius of convergence

Published on 17 Apr 2026 - 8:23

score 324 · Answer 4 · 2026-04-15 09:36:03

324

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Prove that the set $\{x_n:n\in\mathbb{N}\}\cup\{a\}$ is sequentially compact using sequences

Published on 15 Apr 2026 - 9:36

score 2.6k · Answer 5 · 2026-04-11 17:11:41

2.6k

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Convergent and Cauchy sequences in metric spaces

Published on 11 Apr 2026 - 17:11

score 66 · Answer 6 · 2026-04-15 13:15:39

66

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Evaluating whether or not a particular sequence is monotone.

Published on 15 Apr 2026 - 13:15

score 64 · Answer 7 · 2026-04-16 22:42:58

64

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Prove that if $\{a_n\}$ converges to $a$ and $|a|<1$ that $\{a_n^n\}$ converges to $0$.

Published on 16 Apr 2026 - 22:42

score 210 · Answer 8 · 2026-04-12 01:37:11

210

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Do the irrationals form a closed subset of R?

Published on 12 Apr 2026 - 1:37

score 125 · Answer 9 · 2026-04-12 16:44:22

125

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Evaluating infinite series with $a^{(2^n)} + 1$ form denominator

Published on 12 Apr 2026 - 16:44

score 554 · Answer 10 · 2026-04-11 10:50:54

554

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Is subset of convergent sequence bounded?

Published on 11 Apr 2026 - 10:50

score 251 · Answer 11 · 2026-04-19 23:25:03

251

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Why divide a second order differential equation, don't we lose solutions?

Published on 19 Apr 2026 - 23:25

score 481 · Answer 12 · 2026-04-15 14:51:49

481

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If sides $a$, $b$, $c$ of $\triangle ABC$ are in arithmetic progression, then $3\tan\frac{A}{2}\tan\frac {C}{2}=1$

Published on 15 Apr 2026 - 14:51

score 1.3k · Answer 13 · 2026-04-12 00:02:45

1.3k

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Proof Verification: $\lim_{x \to 0} \cos(1/x) $ does not converge

Published on 12 Apr 2026 - 0:02

score 109 · Answer 14 · 2026-04-16 18:03:46

109

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Calculate the following limit: $\lim_{n\to \infty} a_n = \frac{1}{n^5}(1^4 +2^4+....+n^4)$

Published on 16 Apr 2026 - 18:03

score 55 · Answer 15 · 2026-04-14 02:30:59

55

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Is it true that $(A_n)_n \to A \implies (A_{k_n})_n \to A$?

Published on 14 Apr 2026 - 2:30

List Question

Asymptotic behavior of the sequence $u_n=\int_0^1\frac{e^{-t}}{t+\frac{1}{n}}dt$

Calculate the limit of $\left(\frac{n+1}{n-5}\right)^{5n-2}$

$\sum_{n=0}^{\infty}(2+(-1)^n)x^n$ radius of convergence

Prove that the set $\{x_n:n\in\mathbb{N}\}\cup\{a\}$ is sequentially compact using sequences

Convergent and Cauchy sequences in metric spaces

Evaluating whether or not a particular sequence is monotone.

Prove that if $\{a_n\}$ converges to $a$ and $|a|<1$ that $\{a_n^n\}$ converges to $0$.

Do the irrationals form a closed subset of R?

Evaluating infinite series with $a^{(2^n)} + 1$ form denominator

Is subset of convergent sequence bounded?

Why divide a second order differential equation, don't we lose solutions?

If sides $a$, $b$, $c$ of $\triangle ABC$ are in arithmetic progression, then $3\tan\frac{A}{2}\tan\frac {C}{2}=1$

Proof Verification: $\lim_{x \to 0} \cos(1/x) $ does not converge

Calculate the following limit: $\lim_{n\to \infty} a_n = \frac{1}{n^5}(1^4 +2^4+....+n^4)$

Is it true that $(A_n)_n \to A \implies (A_{k_n})_n \to A$?

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