Question

Prove that a power series that is zero on a sequence that converges to zero is the zero function

score 1.9k · Answer 1 · 2026-04-14 18:08:50

1.9k

Views

Prove that a power series that is zero on a sequence that converges to zero is the zero function

Published on 14 Apr 2026 - 18:08

score 2.6k · Answer 2 · 2026-04-16 21:24:28

2.6k

Views

True or false, prove or find a counterexample. If $\{x_n\}$ is a sequence such that $\{x_n^2\}$ converges, then $\{x_n\}$ converges

Published on 16 Apr 2026 - 21:24

score 76 · Answer 3 · 2026-04-09 03:41:11

76

Views

What about an approximation of the Hölder's constant associated to $\sum_{n=0}^\infty\gamma^n\cos(11^n\pi x)$, where $\gamma$ is the Euler's constant?

Published on 09 Apr 2026 - 3:41

score 912 · Answer 4 · 2026-04-15 13:21:56

912

Views

Number of unique sequences up to permutation

Published on 15 Apr 2026 - 13:21

score 184 · Answer 5 · 2026-04-11 19:38:34

184

Views

Closure of A consist of every point of A including the set of all limits of convergent subsequences of A.

Published on 11 Apr 2026 - 19:38

score 210 · Answer 6 · 2026-04-11 04:13:52

210

Views

Does $\sum^n_{k=1} (-1)^k$ converge for even $n$?

Published on 11 Apr 2026 - 4:13

score 35 · Answer 7 · 2026-04-14 11:08:25

35

Views

Can we find any realization of the Bolzano Weierstrass theorem?

Published on 14 Apr 2026 - 11:08

score 87 · Answer 8 · 2026-04-14 19:14:37

87

Views

Find a simple sequence that is asymptotically equivalent to $u_n = \sum_{k=n+1}^{+\infty} \frac{\ln{k}}{k^2}$

Published on 14 Apr 2026 - 19:14

score 752 · Answer 9 · 2026-04-09 02:24:22

752

Views

Pointwise limit of continuous functions, but not Riemann integrable.

Published on 09 Apr 2026 - 2:24

score 267 · Answer 10 · 2026-04-16 16:09:05

267

Views

Criterion equivalent to a sequence being Cauchy?

Published on 16 Apr 2026 - 16:09

score 106 · Answer 11 · 2026-04-16 14:20:05

106

Views

Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer

Published on 16 Apr 2026 - 14:20

score 99 · Answer 12 · 2026-04-17 07:54:06

99

Views

Show that if $\lim(x_n - x_{n-2}) = 0$ then $\lim(\frac{x_n - x_{n-1}}{n}) = 0$

Published on 17 Apr 2026 - 7:54

score 145 · Answer 13 · 2026-04-16 16:10:27

145

Views

Proof $\frac{\log(n!)}{n\log n}$ is increasing for positive integer $n$ ($\log n=\ln(n)$)

Published on 16 Apr 2026 - 16:10

score 195 · Answer 14 · 2026-04-13 03:27:50

195

Views

Flawed proof that $\sum_{n=3}^\infty \frac{1}{n\ln{n}(\ln{(\ln{n})})}$ converges.

Published on 13 Apr 2026 - 3:27

score 370 · Answer 15 · 2026-04-17 05:24:09

370

Views

Prove $\sum\limits_{n=0}^\infty\frac{5^n(3^{5^{n+1}}-5\cdot3^{5^n}+4)}{(729)^{5^n}-(243)^{5^n}-5\cdot3^{5^n}+1}=\frac12$

Published on 17 Apr 2026 - 5:24

List Question

Prove that a power series that is zero on a sequence that converges to zero is the zero function

True or false, prove or find a counterexample. If $\{x_n\}$ is a sequence such that $\{x_n^2\}$ converges, then $\{x_n\}$ converges

What about an approximation of the Hölder's constant associated to $\sum_{n=0}^\infty\gamma^n\cos(11^n\pi x)$, where $\gamma$ is the Euler's constant?

Number of unique sequences up to permutation

Closure of A consist of every point of A including the set of all limits of convergent subsequences of A.

Does $\sum^n_{k=1} (-1)^k$ converge for even $n$?

Can we find any realization of the Bolzano Weierstrass theorem?

Find a simple sequence that is asymptotically equivalent to $u_n = \sum_{k=n+1}^{+\infty} \frac{\ln{k}}{k^2}$

Pointwise limit of continuous functions, but not Riemann integrable.

Criterion equivalent to a sequence being Cauchy?

Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer

Show that if $\lim(x_n - x_{n-2}) = 0$ then $\lim(\frac{x_n - x_{n-1}}{n}) = 0$

Proof $\frac{\log(n!)}{n\log n}$ is increasing for positive integer $n$ ($\log n=\ln(n)$)

Flawed proof that $\sum_{n=3}^\infty \frac{1}{n\ln{n}(\ln{(\ln{n})})}$ converges.

Prove $\sum\limits_{n=0}^\infty\frac{5^n(3^{5^{n+1}}-5\cdot3^{5^n}+4)}{(729)^{5^n}-(243)^{5^n}-5\cdot3^{5^n}+1}=\frac12$

Trending Questions

Popular # Hahtags

Popular Questions