Question

How to show $\sum\limits_{i=1}^{t}\frac{1}{i}2^{t-i}=2^t\ln 2 -\frac{1}{2}\sum\limits_{k=0}^\infty \frac{1}{2^k(k+t+1)}$

score 36 · Answer 1 · 2016-03-13 11:04:56

36

Views

How to show $\sum\limits_{i=1}^{t}\frac{1}{i}2^{t-i}=2^t\ln 2 -\frac{1}{2}\sum\limits_{k=0}^\infty \frac{1}{2^k(k+t+1)}$

Published on 13 Mar 2016 - 11:04

score 3.3k · Answer 2 · 2016-03-13 17:32:30

3.3k

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Surface area of rotating curve about $x$-axis: $y=(x+1)^{1/2}$

Published on 13 Mar 2016 - 17:32

score 89 · Answer 3 · 2016-03-14 11:24:00

89

Views

Closed form of this expression

Published on 14 Mar 2016 - 11:24

score 253 · Answer 4 · 2026-04-04 06:02:56

253

Views

closed form for $I(n)=\int_0^1\left ( \frac{\pi}{4}-\arctan x \right )^n\frac{1+x}{1-x}\frac{dx}{1+x^2}$

Published on 04 Apr 2026 - 6:02

score 1.4k · Answer 5 · 2026-04-02 11:13:17

1.4k

Views

Closed form of Baker Campbell Hausdorff theorem with cyclic bracket structure

Published on 02 Apr 2026 - 11:13

score 180 · Answer 6 · 2016-03-16 00:16:29

180

Views

Does a closed form solution exist for $x$?

Published on 16 Mar 2016 - 0:16

score 211 · Answer 7 · 2016-03-16 15:27:49

211

Views

Find closed formula for the recurrence $a_{n}=na_{n-1}+n(n-1)a_{n-2}$

Published on 16 Mar 2016 - 15:27

score 91 · Answer 8 · 2016-03-16 15:51:12

91

Views

Find closed formula for $a_{n+1}=(n+1)a_{n}+n!$

Published on 16 Mar 2016 - 15:51

score 86 · Answer 9 · 2026-04-01 04:54:59

86

Views

Solve an equation in which a variable is an argument of a tangent: $x= K+y\tan(\sqrt{y})+y$

Published on 01 Apr 2026 - 4:54

score 886 · Answer 10 · 2016-03-17 08:30:09

886

Views

Evaluate $\int_0^1\int_0^1 \left\{ \frac{e^x}{e^y} \right\}dxdy$

Published on 17 Mar 2016 - 8:30

score 251 · Answer 11 · 2016-03-20 15:41:49

251

Views

Classifying functions whose inverse do not have a closed form

Published on 20 Mar 2016 - 15:41

score 725 · Answer 12 · 2016-03-20 19:24:19

725

Views

Closed form for $\sum_{n=1}^\infty \int_0^1 \frac{x^{n-1}\ln^2(x)\ln(1-x)}{n^2} \,dx$

Published on 20 Mar 2016 - 19:24

score 77 · Answer 13 · 2026-04-01 04:51:55

77

Views

Closed form expression for $x$

Published on 01 Apr 2026 - 4:51

score 223 · Answer 14 · 2026-04-01 04:57:39

223

Views

Does there exist a closed form expression for roots of polynomials of the form $x^n + bx + c$

Published on 01 Apr 2026 - 4:57

score 128 · Answer 15 · 2016-03-22 12:24:47

128

Views

Find the closed formula for following problem.

Published on 22 Mar 2016 - 12:24

List Question

How to show $\sum\limits_{i=1}^{t}\frac{1}{i}2^{t-i}=2^t\ln 2 -\frac{1}{2}\sum\limits_{k=0}^\infty \frac{1}{2^k(k+t+1)}$

Surface area of rotating curve about $x$-axis: $y=(x+1)^{1/2}$

Closed form of this expression

closed form for $I(n)=\int_0^1\left ( \frac{\pi}{4}-\arctan x \right )^n\frac{1+x}{1-x}\frac{dx}{1+x^2}$

Closed form of Baker Campbell Hausdorff theorem with cyclic bracket structure

Does a closed form solution exist for $x$?

Find closed formula for the recurrence $a_{n}=na_{n-1}+n(n-1)a_{n-2}$

Find closed formula for $a_{n+1}=(n+1)a_{n}+n!$

Solve an equation in which a variable is an argument of a tangent: $x= K+y\tan(\sqrt{y})+y$

Evaluate $\int_0^1\int_0^1 \left\{ \frac{e^x}{e^y} \right\}dxdy$

Classifying functions whose inverse do not have a closed form

Closed form for $\sum_{n=1}^\infty \int_0^1 \frac{x^{n-1}\ln^2(x)\ln(1-x)}{n^2} \,dx$

Closed form expression for $x$

Does there exist a closed form expression for roots of polynomials of the form $x^n + bx + c$

Find the closed formula for following problem.

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