Question

Is there any geometry behind the Basel problem?

score 522 · Answer 1 · 2026-04-13 15:08:00

522

Views

Is there any geometry behind the Basel problem?

Published on 13 Apr 2026 - 15:08

score 74 · Answer 2 · 2026-04-16 08:43:17

74

Views

Prove that the series $\sum \frac{a_n}{r_n}$ diverges.

Published on 16 Apr 2026 - 8:43

score 317 · Answer 3 · 2026-04-17 05:17:33

317

Views

A very challenging question integral of an infinite product.

Published on 17 Apr 2026 - 5:17

score 43 · Answer 4 · 2026-04-16 01:09:18

43

Views

Studying the convergence of $(x _n)_{n\geqslant1}$, $(n^k x _n)_{n\geqslant1}$, $\ k>0$

Published on 16 Apr 2026 - 1:09

score 372 · Answer 5 · 2026-04-18 07:51:40

372

Views

Radius of convergence of Cauchy product – examples

Published on 18 Apr 2026 - 7:51

score 371 · Answer 6 · 2026-04-15 13:51:51

371

Views

$\sum\limits_{n=1}^{\infty}\frac{\sin(nx)}{{(n^4+x^4)}^{\frac{1}{3}}}$ How to major $\sum\limits_{n=1}^{\infty}{\sin(nx)}$?

Published on 15 Apr 2026 - 13:51

score 47 · Answer 7 · 2026-04-11 04:06:18

47

Views

Determining convergence of series of functions with natural logarithm

Published on 11 Apr 2026 - 4:06

score 55 · Answer 8 · 2026-04-15 13:44:16

55

Views

Limit of an integral sequence

Published on 15 Apr 2026 - 13:44

score 240 · Answer 9 · 2026-04-17 14:03:32

240

Views

Growth of the sequence given by $x_0=1, x_{n+1}=\sqrt{x_n^2+\frac{1}{x_n^2}}$

Published on 17 Apr 2026 - 14:03

score 304 · Answer 10 · 2026-04-09 04:14:36

304

Views

If for any $k$, $\sum\limits_{n=0}^\infty a_n^k=\sum\limits_{n=0}^\infty b_n^k$, then$(a_n)=(b_{σ(n)}),\ σ \in{\mathfrak S}_{\mathbb N}$

Published on 09 Apr 2026 - 4:14

score 80 · Answer 11 · 2026-04-16 02:30:48

80

Views

$\sum_\limits{n=1}^{\infty}\frac{n}{x^n}$ ratio or root test? different results?

Published on 16 Apr 2026 - 2:30

score 104 · Answer 12 · 2026-04-14 22:08:41

104

Views

$\lim_{n\to\infty}\int_0^1\sin (2 \pi nx)\, \mathrm{e}^{-\sqrt{x}}dx=0$

Published on 14 Apr 2026 - 22:08

score 68 · Answer 13 · 2026-04-16 00:40:12

68

Views

Prove that $\lim_{y \to x-}f(y) = a$ if for every sequence $(x_n)_n$ in $\mathbb{R}$ that increases towards x, the sequence $f(x_n)$ converges to $a$

Published on 16 Apr 2026 - 0:40

score 41 · Answer 14 · 2026-04-13 06:59:35

41

Views

Derivative of Sereis

Published on 13 Apr 2026 - 6:59

score 116 · Answer 15 · 2026-04-11 19:45:40

116

Views

Studying convergence of $\sum\limits_{k=1}^{\infty}\frac{k!\exp(k)}{(k+1)^k}$

Published on 11 Apr 2026 - 19:45

List Question

Is there any geometry behind the Basel problem?

Prove that the series $\sum \frac{a_n}{r_n}$ diverges.

A very challenging question integral of an infinite product.

Studying the convergence of $(x _n)_{n\geqslant1}$, $(n^k x _n)_{n\geqslant1}$, $\ k>0$

Radius of convergence of Cauchy product – examples

$\sum\limits_{n=1}^{\infty}\frac{\sin(nx)}{{(n^4+x^4)}^{\frac{1}{3}}}$ How to major $\sum\limits_{n=1}^{\infty}{\sin(nx)}$?

Determining convergence of series of functions with natural logarithm

Limit of an integral sequence

Growth of the sequence given by $x_0=1, x_{n+1}=\sqrt{x_n^2+\frac{1}{x_n^2}}$

If for any $k$, $\sum\limits_{n=0}^\infty a_n^k=\sum\limits_{n=0}^\infty b_n^k$, then$(a_n)=(b_{σ(n)}),\ σ \in{\mathfrak S}_{\mathbb N}$

$\sum_\limits{n=1}^{\infty}\frac{n}{x^n}$ ratio or root test? different results?

$\lim_{n\to\infty}\int_0^1\sin (2 \pi nx)\, \mathrm{e}^{-\sqrt{x}}dx=0$

Prove that $\lim_{y \to x-}f(y) = a$ if for every sequence $(x_n)_n$ in $\mathbb{R}$ that increases towards x, the sequence $f(x_n)$ converges to $a$

Derivative of Sereis

Studying convergence of $\sum\limits_{k=1}^{\infty}\frac{k!\exp(k)}{(k+1)^k}$

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