Question

Proving $\int_\limits{a}^{b}F(x)dx=\sum_\limits{n=k}^{\infty}\int_\limits{a}^{b}f_n(x)dx$

score 72 · Answer 1 · 2026-04-16 12:23:11

72

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Proving $\int_\limits{a}^{b}F(x)dx=\sum_\limits{n=k}^{\infty}\int_\limits{a}^{b}f_n(x)dx$

Published on 16 Apr 2026 - 12:23

score 280 · Answer 2 · 2026-05-11 06:11:59

280

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Fibonacci-type Sequence with Complex Numbers

Published on 11 May 2026 - 6:11

score 269 · Answer 3 · 2026-05-10 15:50:46

269

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Fractional part of the floor function Integral

Published on 10 May 2026 - 15:50

score 209 · Answer 4 · 2026-04-14 09:28:25

209

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Find $t$ such that $\lim_{n\to\infty} \frac {\sum_{r=1}^n r^4\cdot\sum_{r=1}^n r^5}{\sum_{r=1}^n r^t\cdot\sum_{r=1}^n r^{9-t}}=\frac 45$

Published on 14 Apr 2026 - 9:28

score 52 · Answer 5 · 2026-04-11 15:50:04

52

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Technical Inequality needed to establish smooth but nowhere analytic function

Published on 11 Apr 2026 - 15:50

score 295 · Answer 6 · 2026-04-16 00:01:17

295

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Show that $\sum_{n=1}^{\infty} \frac{(2n)!}{4^n(n!)^2}$ is divergent

Published on 16 Apr 2026 - 0:01

score 734 · Answer 7 · 2026-04-13 16:01:25

734

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upper bound of p-series

Published on 13 Apr 2026 - 16:01

score 47 · Answer 8 · 2026-04-14 01:56:56

47

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Showing $\rho = -1 + \int_0^\infty \frac{e^{-y}}{1+\delta y} \ dy = \sum_{k=1}^\infty (-1)^k \delta^k k!$

Published on 14 Apr 2026 - 1:56

score 445 · Answer 9 · 2026-04-08 20:35:17

445

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Abel Summation Formula

Published on 08 Apr 2026 - 20:35

score 973 · Answer 10 · 2026-04-13 20:13:15

973

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Proving Countable Additivity From Finite Additivity

Published on 13 Apr 2026 - 20:13

score 4.6k · Answer 11 · 2026-04-16 11:07:56

4.6k

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Prove that $x_{n+1}=\frac{1}{4-x_n}$ converges

Published on 16 Apr 2026 - 11:07

score 452 · Answer 12 · 2026-04-14 15:11:25

452

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Taking the derivative of $\sum_\limits{n=1}^{\infty}\arctan(\frac{x}{n^2})$

Published on 14 Apr 2026 - 15:11

score 177 · Answer 13 · 2026-04-17 08:01:38

177

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Give an asymptotic developement of $I_n=\int_0^1 (x^{n}-x^{n-2})\ln(1+x^n)dx.$

Published on 17 Apr 2026 - 8:01

score 100 · Answer 14 · 2026-04-15 23:48:24

100

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Why $f(x)=\sum_{n=0}^\infty \frac{f^{(n)}(0)\, x^n}{n!} $?

Published on 15 Apr 2026 - 23:48

score 105 · Answer 15 · 2026-04-13 22:53:06

105

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Why $ \sum_{k=1}^{\infty}\frac{1}{k^{1+x}} $ is not uniformly convergent on $ \left(0,\;+\infty\right) $

Published on 13 Apr 2026 - 22:53

List Question

Proving $\int_\limits{a}^{b}F(x)dx=\sum_\limits{n=k}^{\infty}\int_\limits{a}^{b}f_n(x)dx$

Fibonacci-type Sequence with Complex Numbers

Fractional part of the floor function Integral

Find $t$ such that $\lim_{n\to\infty} \frac {\sum_{r=1}^n r^4\cdot\sum_{r=1}^n r^5}{\sum_{r=1}^n r^t\cdot\sum_{r=1}^n r^{9-t}}=\frac 45$

Technical Inequality needed to establish smooth but nowhere analytic function

Show that $\sum_{n=1}^{\infty} \frac{(2n)!}{4^n(n!)^2}$ is divergent

upper bound of p-series

Showing $\rho = -1 + \int_0^\infty \frac{e^{-y}}{1+\delta y} \ dy = \sum_{k=1}^\infty (-1)^k \delta^k k!$

Abel Summation Formula

Proving Countable Additivity From Finite Additivity

Prove that $x_{n+1}=\frac{1}{4-x_n}$ converges

Taking the derivative of $\sum_\limits{n=1}^{\infty}\arctan(\frac{x}{n^2})$

Give an asymptotic developement of $I_n=\int_0^1 (x^{n}-x^{n-2})\ln(1+x^n)dx.$

Why $f(x)=\sum_{n=0}^\infty \frac{f^{(n)}(0)\, x^n}{n!} $?

Why $ \sum_{k=1}^{\infty}\frac{1}{k^{1+x}} $ is not uniformly convergent on $ \left(0,\;+\infty\right) $

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