Question

How do you get from $\sum\limits_{i=0}^{n}{i\cdot 2^i}$ to $2(n-1)\cdot 2^n+2$?

score 96 · Answer 1 · 2026-04-16 07:08:46

96

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How do you get from $\sum\limits_{i=0}^{n}{i\cdot 2^i}$ to $2(n-1)\cdot 2^n+2$?

Published on 16 Apr 2026 - 7:08

score 191 · Answer 2 · 2026-04-15 05:50:41

191

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How to evaluate $\int_0^1 -\frac {\ln(1-x)}{x}dx$

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score 102 · Answer 3 · 2026-04-30 01:08:54

102

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Apostol's proof for the method of exhaustion

Published on 30 Apr 2026 - 1:08

score 45 · Answer 4 · 2026-04-15 20:03:49

45

Views

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score 122 · Answer 5 · 2026-04-13 12:44:49

122

Views

Solving a limit sum involving Cantor sets

Published on 13 Apr 2026 - 12:44

score 152 · Answer 6 · 2026-03-25 04:43:51

152

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For $a,b,c\in\left[\frac{1}{\sqrt{6}}, 6\right]$: $\sum_{cyc}\frac{4}{a+3b}\geq \sum_{cyc}\frac{3}{a+2b}$

Published on 25 Mar 2026 - 4:43

score 99 · Answer 7 · 2026-04-23 01:53:29

99

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How do I represent this sequence: $ 0,0,1,1,2,2,3,3, \dots$?

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score 74 · Answer 8 · 2026-04-13 10:24:01

74

Views

The number of ways to have a sum of $n$ natural numbers equal to $k$

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score 52 · Answer 9 · 2026-03-25 09:23:48

52

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Published on 25 Mar 2026 - 9:23

score 213 · Answer 10 · 2026-04-14 10:54:10

213

Views

Find the convergence/divergence of a recursive formula that involves a summation of all previous terms

Published on 14 Apr 2026 - 10:54

score 712 · Answer 11 · 2026-04-15 03:50:02

712

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A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations

Published on 15 Apr 2026 - 3:50

score 49 · Answer 12 · 2026-04-11 13:31:26

49

Views

Finding the numerical approximation for the derivative $F ′ ( x )$ without the actual function

Published on 11 Apr 2026 - 13:31

score 50 · Answer 13 · 2026-04-10 04:10:22

50

Views

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Published on 10 Apr 2026 - 4:10

score 58 · Answer 14 · 2026-04-09 13:48:11

58

Views

Transience of random walk on the integers - Sum estimation

Published on 09 Apr 2026 - 13:48

score 149 · Answer 15 · 2026-04-12 09:20:46

149

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general form of coefficients in partial fraction decomposition

Published on 12 Apr 2026 - 9:20

List Question

How do you get from $\sum\limits_{i=0}^{n}{i\cdot 2^i}$ to $2(n-1)\cdot 2^n+2$?

How to evaluate $\int_0^1 -\frac {\ln(1-x)}{x}dx$

Apostol's proof for the method of exhaustion

Using summation to calculate the remainder of order 3 of a multivariable function

Solving a limit sum involving Cantor sets

For $a,b,c\in\left[\frac{1}{\sqrt{6}}, 6\right]$: $\sum_{cyc}\frac{4}{a+3b}\geq \sum_{cyc}\frac{3}{a+2b}$

How do I represent this sequence: $ 0,0,1,1,2,2,3,3, \dots$?

The number of ways to have a sum of $n$ natural numbers equal to $k$

Closed form for the function $G(x) = \sum_{n=1}^\infty (e^{x/n²}-1) $

Find the convergence/divergence of a recursive formula that involves a summation of all previous terms

A suprising conjectural closed-form of $\sum _{n=1}^{\infty } \frac{1}{n^4 2^n \binom{3 n}{n}}$ and integral variations

Finding the numerical approximation for the derivative $F ′ ( x )$ without the actual function

Simplify a series involving binomial coefficients

Transience of random walk on the integers - Sum estimation

general form of coefficients in partial fraction decomposition

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