Question

Show that if $\sum_{n=0}^{\infty}a_n^k=\sum_{n=0}^{\infty}b_n^k$ for all $k\in \Bbb N^*$ then $(a_n) = (b_n)$

score 224 · Answer 1 · 2026-05-01 01:10:33

224

Views

Show that if $\sum_{n=0}^{\infty}a_n^k=\sum_{n=0}^{\infty}b_n^k$ for all $k\in \Bbb N^*$ then $(a_n) = (b_n)$

Published on 01 May 2026 - 1:10

score 84 · Answer 2 · 2026-04-15 21:32:53

84

Views

Series $\sum_{n=1}^{\infty}(1-\frac2n)^{-n^2}\frac1{e^{2n}}$

Published on 15 Apr 2026 - 21:32

score 109 · Answer 3 · 2026-04-11 01:28:10

109

Views

Finding limit for infinite quantities.

Published on 11 Apr 2026 - 1:28

score 69 · Answer 4 · 2026-04-14 03:17:24

69

Views

How are these prime numbers occuring here?

Published on 14 Apr 2026 - 3:17

score 48 · Answer 5 · 2026-04-14 23:47:52

48

Views

Link between interpolation and numerical series

Published on 14 Apr 2026 - 23:47

score 1.1k · Answer 6 · 2026-04-14 18:21:02

1.1k

Views

$u_{n+2}=\sqrt{u_{n+1}u_{n}}$ find limit of $\{u_n\}$

Published on 14 Apr 2026 - 18:21

score 121 · Answer 7 · 2026-04-14 22:53:04

121

Views

Is the series $\sum_{n=1}^{\infty} \Bigl(1-\Bigl(1-\frac{1}{n^{1+\epsilon}}\Bigr)^n\Bigr)$ convergent?

Published on 14 Apr 2026 - 22:53

score 139 · Answer 8 · 2026-04-15 07:04:31

139

Views

Error on MathWorld: $\sum_{n=1}^\infty (\zeta(4n)-1) = \frac{1}{8}(7-2\coth \pi)$

Published on 15 Apr 2026 - 7:04

score 30 · Answer 9 · 2026-04-11 06:10:22

30

Views

How to simplify an expression with a sequence of products within a sequence of sums.

Published on 11 Apr 2026 - 6:10

score 51 · Answer 10 · 2026-03-30 02:05:45

51

Views

Proof about sequences and $\epsilon-$ inequalities in a compact set $X$

Published on 30 Mar 2026 - 2:05

score 65 · Answer 11 · 2026-04-15 09:27:47

65

Views

Is my solution for the divergence of this series correct?

Published on 15 Apr 2026 - 9:27

score 184 · Answer 12 · 2026-04-14 19:32:33

184

Views

Consider the polynomial equation $x^{5}-x-1=0$

Published on 14 Apr 2026 - 19:32

score 138 · Answer 13 · 2026-04-17 12:46:22

138

Views

How to determine whether the sum ${\sum}_{k=1}^{\infty} {\sin(2^k)\over k}$ converges?

Published on 17 Apr 2026 - 12:46

score 987 · Answer 14 · 2026-04-17 01:30:16

987

Views

Sequences $x_{n+1}=\frac{x_n+y_n}2 $ and $ y_{n+1}=\frac{2x_ny_n}{x_n+y_n}$

Published on 17 Apr 2026 - 1:30

score 236 · Answer 15 · 2026-04-18 13:37:16

236

Views

Prove that a strictly monontone increasing sequence in $\Bbb{N}$ is greater or equal than its index.

Published on 18 Apr 2026 - 13:37

List Question

Show that if $\sum_{n=0}^{\infty}a_n^k=\sum_{n=0}^{\infty}b_n^k$ for all $k\in \Bbb N^*$ then $(a_n) = (b_n)$

Series $\sum_{n=1}^{\infty}(1-\frac2n)^{-n^2}\frac1{e^{2n}}$

Finding limit for infinite quantities.

How are these prime numbers occuring here?

Link between interpolation and numerical series

$u_{n+2}=\sqrt{u_{n+1}u_{n}}$ find limit of $\{u_n\}$

Is the series $\sum_{n=1}^{\infty} \Bigl(1-\Bigl(1-\frac{1}{n^{1+\epsilon}}\Bigr)^n\Bigr)$ convergent?

Error on MathWorld: $\sum_{n=1}^\infty (\zeta(4n)-1) = \frac{1}{8}(7-2\coth \pi)$

How to simplify an expression with a sequence of products within a sequence of sums.

Proof about sequences and $\epsilon-$ inequalities in a compact set $X$

Is my solution for the divergence of this series correct?

Consider the polynomial equation $x^{5}-x-1=0$

How to determine whether the sum ${\sum}_{k=1}^{\infty} {\sin(2^k)\over k}$ converges?

Sequences $x_{n+1}=\frac{x_n+y_n}2 $ and $ y_{n+1}=\frac{2x_ny_n}{x_n+y_n}$

Prove that a strictly monontone increasing sequence in $\Bbb{N}$ is greater or equal than its index.

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