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Example of a differentiable $S(x)=\sum f_n(x)$ such that $S'(x)\ne\sum f_n'(x)$ for (at least almost) all x

score 145 · Answer 1 · 2026-04-16 04:18:34

145

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Example of a differentiable $S(x)=\sum f_n(x)$ such that $S'(x)\ne\sum f_n'(x)$ for (at least almost) all x

Published on 16 Apr 2026 - 4:18

score 50 · Answer 2 · 2026-04-15 17:56:17

50

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If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

Published on 15 Apr 2026 - 17:56

score 622 · Answer 3 · 2026-04-16 23:22:50

622

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Proving $a_{n+1}^2=a_n·a_{n+2}+(-1)^n$ for Fibonacci sequence $\{a_n\}$

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score 30 · Answer 4 · 2026-04-09 12:28:58

30

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2.1k

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score 564 · Answer 6 · 2026-04-14 20:26:00

564

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score 52 · Answer 7 · 2026-04-11 09:01:37

52

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score 56 · Answer 8 · 2026-04-14 08:30:10

56

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score 220 · Answer 9 · 2026-04-12 02:41:09

220

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score 65 · Answer 10 · 2026-04-17 13:31:44

65

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An asymptotic about the recurrence $a_{n+1}=n\varphi(a_n)+a_{\varphi(n)}$, with $a_1=1$ and being $\varphi(m)$ the Euler's totient function

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score 482 · Answer 11 · 2026-04-17 00:40:28

482

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Show if the series $\sum _{n=1}^{\infty} \frac {3}{9n+1}$ converges or diverges.

Published on 17 Apr 2026 - 0:40

score 75 · Answer 12 · 2026-04-13 15:07:51

75

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score 63 · Answer 13 · 2026-04-11 11:13:17

63

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score 204 · Answer 14 · 2026-04-12 16:33:15

204

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score 687 · Answer 15 · 2026-04-15 06:40:37

687

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Convergence of $\sum\frac{1}{n(\log(n))^c}$

Published on 15 Apr 2026 - 6:40

List Question

Example of a differentiable $S(x)=\sum f_n(x)$ such that $S'(x)\ne\sum f_n'(x)$ for (at least almost) all x

If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

Proving $a_{n+1}^2=a_n·a_{n+2}+(-1)^n$ for Fibonacci sequence $\{a_n\}$

simplifying an equation with fractions

Collection of standard facts about convergence of random variables

Prove that $\sum_{n=0}^\infty\frac{\cos (n^2x)}{2^{nx}}$ is continuous for $x> 0$

How derive a closed formula for $\sum_{k\ge 0} \binom{n}{a+rk}$

How this series is bounded

Does the series $\sum \frac{\sin p}{p}$, where $p$ prime, converge?

An asymptotic about the recurrence $a_{n+1}=n\varphi(a_n)+a_{\varphi(n)}$, with $a_1=1$ and being $\varphi(m)$ the Euler's totient function

Show if the series $\sum _{n=1}^{\infty} \frac {3}{9n+1}$ converges or diverges.

Characteristic of zeroes of a power series

Standard notion for sequence of polynomial terms exponents

olympic mathematics

Convergence of $\sum\frac{1}{n(\log(n))^c}$

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