Question

Is it correct to state that a sum series converges as long as the partial sums do as well?

score 104 · Answer 1 · 2026-04-16 05:42:43

104

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Is it correct to state that a sum series converges as long as the partial sums do as well?

Published on 16 Apr 2026 - 5:42

score 83 · Answer 2 · 2026-04-14 21:48:10

83

Views

Suppose that for all $i \le k$, one knows a polynomial $f_i$ such that $f_i(x) = x^i$, calculate $f_{k+1}$

Published on 14 Apr 2026 - 21:48

score 367 · Answer 3 · 2026-04-17 15:41:07

367

Views

Integral $\int_{0}^{1} \frac{\ln^2 x \ln^2 (1+x)\ln^2(1-x)}{x^2}dx$

Published on 17 Apr 2026 - 15:41

score 1.8k · Answer 4 · 2026-04-15 02:37:32

1.8k

Views

Sums of pairwise different prime numbers

Published on 15 Apr 2026 - 2:37

score 149 · Answer 5 · 2026-04-15 05:04:35

149

Views

Root, divergence of hypergeometric function $1F1$

Published on 15 Apr 2026 - 5:04

score 50 · Answer 6 · 2026-04-16 22:52:35

50

Views

Show that $(1c_1 + c_2) + (2c_1 + c_2) + ... + (nc_1 + c_2)=\frac{c_1n(n+1)}{2} +nc_2$

Published on 16 Apr 2026 - 22:52

score 49 · Answer 7 · 2026-04-17 02:48:20

49

Views

proving or refuting the convergence of a digital sequence

Published on 17 Apr 2026 - 2:48

score 193 · Answer 8 · 2026-04-14 02:14:19

193

Views

Abel's lemma confusion

Published on 14 Apr 2026 - 2:14

score 477 · Answer 9 · 2026-04-15 05:23:18

477

Views

Sum of even digits

Published on 15 Apr 2026 - 5:23

score 104 · Answer 10 · 2026-04-12 14:41:48

104

Views

Showing that $\sum\limits_{r=0}^n({1 \over r!} \sum\limits_{s=0}^{n-r}{(-1)^s \over s!}) = 1$

Published on 12 Apr 2026 - 14:41

score 338 · Answer 11 · 2026-04-15 06:23:22

338

Views

Find $\sum\limits_{k=0}^{n-1}\,\omega_n^{k^2\ell}$, where $\omega_n:=\exp\left(\frac{2\pi\text{i}}{n}\right)$.

Published on 15 Apr 2026 - 6:23

score 96 · Answer 12 · 2026-04-09 09:56:02

96

Views

an equation with generalized sum

Published on 09 Apr 2026 - 9:56

score 1.1k · Answer 13 · 2026-04-16 14:19:45

1.1k

Views

A closed form of the double sum $\sum_{m=1}^{\infty}\sum_{n=0}^{m-1}\frac{(-1)^{m-n}}{(m^2-n^2)^2} $

Published on 16 Apr 2026 - 14:19

score 159 · Answer 14 · 2026-04-15 13:00:30

159

Views

I have a algorithm and from the post its time complexity is: $\sum_{k=1}^{n}k\binom nk= n 2^{n-1}$

Published on 15 Apr 2026 - 13:00

score 208 · Answer 15 · 2026-04-14 16:21:35

208

Views

For which $n \in \mathbb{N}$ do we have $\sum\limits^n_{k=0} k^3 = (\sum\limits^n_{k=0} k)^2$?

Published on 14 Apr 2026 - 16:21

List Question

Is it correct to state that a sum series converges as long as the partial sums do as well?

Suppose that for all $i \le k$, one knows a polynomial $f_i$ such that $f_i(x) = x^i$, calculate $f_{k+1}$

Integral $\int_{0}^{1} \frac{\ln^2 x \ln^2 (1+x)\ln^2(1-x)}{x^2}dx$

Sums of pairwise different prime numbers

Root, divergence of hypergeometric function $1F1$

Show that $(1c_1 + c_2) + (2c_1 + c_2) + ... + (nc_1 + c_2)=\frac{c_1n(n+1)}{2} +nc_2$

proving or refuting the convergence of a digital sequence

Abel's lemma confusion

Sum of even digits

Showing that $\sum\limits_{r=0}^n({1 \over r!} \sum\limits_{s=0}^{n-r}{(-1)^s \over s!}) = 1$

Find $\sum\limits_{k=0}^{n-1}\,\omega_n^{k^2\ell}$, where $\omega_n:=\exp\left(\frac{2\pi\text{i}}{n}\right)$.

an equation with generalized sum

A closed form of the double sum $\sum_{m=1}^{\infty}\sum_{n=0}^{m-1}\frac{(-1)^{m-n}}{(m^2-n^2)^2} $

I have a algorithm and from the post its time complexity is: $\sum_{k=1}^{n}k\binom nk= n 2^{n-1}$

For which $n \in \mathbb{N}$ do we have $\sum\limits^n_{k=0} k^3 = (\sum\limits^n_{k=0} k)^2$?

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