Question

Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$

score 797 · Answer 1 · 2026-04-05 07:10:21

797

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Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$

Published on 05 Apr 2026 - 7:10

score 3.2k · Answer 2 · 2016-03-23 06:55:55

3.2k

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Find the value of $\int_1^4 xf''(x)dx$ when $f(1) = 2$, $f(4) = 7$, $f'(1) = 5$, $f'(4) = 3$, and $f''$ is continuous

Published on 23 Mar 2016 - 6:55

score 624 · Answer 3 · 2016-03-24 21:28:02

624

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How to integrate $\int\limits_{0}^{\pi/2}\frac{dx}{\cos^3{x}+\sin^3{x}}$?

Published on 24 Mar 2016 - 21:28

score 258 · Answer 4 · 2016-03-25 14:39:27

258

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Find $\lim_{a\to \infty}\frac{1}{a}\int_0^{\infty}\frac{x^2+ax+1}{1+x^4}\cdot\arctan(\frac{1}{x})dx$

Published on 25 Mar 2016 - 14:39

score 88 · Answer 5 · 2016-03-27 02:58:36

88

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How do I find a closed form for this recurrence?

Published on 27 Mar 2016 - 2:58

score 965 · Answer 6 · 2016-03-27 20:29:17

965

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Determine whether $-7 + \frac {14} 3 - \frac {28} 9 + \frac {56} {27} + \dots$ converges or not.

Published on 27 Mar 2016 - 20:29

score 121 · Answer 7 · 2016-03-27 20:42:40

121

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Evaluating $\int\frac{dx}{(a\sin x+ b\cos x)^2}$, $a\neq 0.$

Published on 27 Mar 2016 - 20:42

score 213 · Answer 8 · 2016-03-28 22:45:06

213

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Is $\sum_{k=0}^{r}\binom{r}{k}(r-k-1)^{r-k}(k-1)^{k-1}+(r-2)^r=0$ right?

Published on 28 Mar 2016 - 22:45

score 180 · Answer 9 · 2016-03-30 19:14:11

180

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Closed Form of $ \int_{0}^{\pi} x^3\ln^8(2\sin{(x)}) dx$

Published on 30 Mar 2016 - 19:14

score 68 · Answer 10 · 2016-04-03 12:59:31

68

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Closed form for an integral involving an inverse square root and a cube

Published on 03 Apr 2016 - 12:59

score 207 · Answer 11 · 2016-04-04 21:53:11

207

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Definite Integral $\int_0^1 \left \{\frac{(-1)^{\lfloor 1/x \rfloor}}{x} \right\}\, dx$

Published on 04 Apr 2016 - 21:53

score 3.1k · Answer 12 · 2016-04-04 22:11:22

3.1k

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Sum of a series $\frac {1}{n^2 - m^2}$ m and n odd, $m \ne n$

Published on 04 Apr 2016 - 22:11

score 227 · Answer 13 · 2026-04-06 04:54:14

227

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Infinite sum over Gamma functions?

Published on 06 Apr 2026 - 4:54

score 268 · Answer 14 · 2016-04-06 09:44:10

268

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Find a function for the infinite sum $\sum_{n=0}^\infty \frac{n}{n+1}x^n$

Published on 06 Apr 2016 - 9:44

score 292 · Answer 15 · 2016-04-06 19:31:24

292

Views

How can I prove by induction that this is a closed form of the Fibonacci sequence?

Published on 06 Apr 2016 - 19:31

List Question

Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$

Find the value of $\int_1^4 xf''(x)dx$ when $f(1) = 2$, $f(4) = 7$, $f'(1) = 5$, $f'(4) = 3$, and $f''$ is continuous

How to integrate $\int\limits_{0}^{\pi/2}\frac{dx}{\cos^3{x}+\sin^3{x}}$?

Find $\lim_{a\to \infty}\frac{1}{a}\int_0^{\infty}\frac{x^2+ax+1}{1+x^4}\cdot\arctan(\frac{1}{x})dx$

How do I find a closed form for this recurrence?

Determine whether $-7 + \frac {14} 3 - \frac {28} 9 + \frac {56} {27} + \dots$ converges or not.

Evaluating $\int\frac{dx}{(a\sin x+ b\cos x)^2}$, $a\neq 0.$

Is $\sum_{k=0}^{r}\binom{r}{k}(r-k-1)^{r-k}(k-1)^{k-1}+(r-2)^r=0$ right?

Closed Form of $ \int_{0}^{\pi} x^3\ln^8(2\sin{(x)}) dx$

Closed form for an integral involving an inverse square root and a cube

Definite Integral $\int_0^1 \left \{\frac{(-1)^{\lfloor 1/x \rfloor}}{x} \right\}\, dx$

Sum of a series $\frac {1}{n^2 - m^2}$ m and n odd, $m \ne n$

Infinite sum over Gamma functions?

Find a function for the infinite sum $\sum_{n=0}^\infty \frac{n}{n+1}x^n$

How can I prove by induction that this is a closed form of the Fibonacci sequence?

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