Question

Why does $2+{{n}\choose{1}}+{{n}\choose{2}}+\ldots+{{n}\choose{n-1}}=(1+1)^n$

score 359 · Answer 1 · 2026-04-03 07:22:04

359

Views

Why does $2+{{n}\choose{1}}+{{n}\choose{2}}+\ldots+{{n}\choose{n-1}}=(1+1)^n$

Published on 03 Apr 2026 - 7:22

score 372 · Answer 2 · 2026-04-12 19:06:44

372

Views

$\sum_{p\le x} \frac{1}{pq}$

Published on 12 Apr 2026 - 19:06

score 681 · Answer 3 · 2026-04-09 19:56:15

681

Views

Trigonometric identity involving sum of "Dirichlet kernel like" fractions

Published on 09 Apr 2026 - 19:56

score 119 · Answer 4 · 2026-04-10 23:55:28

119

Views

How to solve equation $\sum a_i/(x + b_i)=1$?

Published on 10 Apr 2026 - 23:55

score 65 · Answer 5 · 2026-04-12 19:16:09

65

Views

Are these two summations equivalent?

Published on 12 Apr 2026 - 19:16

score 70 · Answer 6 · 2026-04-03 07:22:55

70

Views

How find the sum $2\sum_{k=1}^{\infty}\sum_{i=0}^{2k-1}\frac{\binom{2k}{i}\cdot B_{i}\cdot(m-1)^{2k-i}}{2k(2k-1)m^{2k-1}}$

Published on 03 Apr 2026 - 7:22

score 11.6k · Answer 7 · 2026-04-12 00:14:07

11.6k

Views

How can I define $e^x$ as the value of infinite series?

Published on 12 Apr 2026 - 0:14

score 66 · Answer 8 · 2014-05-01 21:33:19

66

Views

Sum with natural log

Published on 01 May 2014 - 21:33

score 227 · Answer 9 · 2026-04-08 21:17:06

227

Views

Finite Trigonometric Sum

Published on 08 Apr 2026 - 21:17

score 108 · Answer 10 · 2026-03-25 12:21:11

108

Views

Show $ \frac {a^3}{a^2+b^2+c^2-bc}+\frac {b^3}{a^2+b^2+c^2-ca} +\frac {c^3}{a^2+b^2+c^2-ab} \le \frac {(a+b+c)^2 (a^4+b^4+c^4)}{6abc(ab+bc+ca)} $

Published on 25 Mar 2026 - 12:21

score 1.9k · Answer 11 · 2014-05-02 13:59:17

1.9k

Views

Convergence of $\sum_{n=1}^\infty{\frac{sin(5n)}{5^n}}$

Published on 02 May 2014 - 13:59

score 196 · Answer 12 · 2026-04-12 18:34:51

196

Views

summation of infinite series

Published on 12 Apr 2026 - 18:34

score 42 · Answer 13 · 2026-04-10 23:50:56

42

Views

Problem finding explicit function without multiple $\sum$s

Published on 10 Apr 2026 - 23:50

score 22.2k · Answer 14 · 2014-05-02 15:21:19

22.2k

Views

I have the pattern: 1 + 2 + 3 + 4 + 5 + 6, but I need the formula for it

Published on 02 May 2014 - 15:21

score 98 · Answer 15 · 2014-05-02 19:19:30

98

Views

Help me with this sum: $\sum_{i=0}^\infty \frac{n}{\log^2\left(\frac{n}{5^i}\right)}$

Published on 02 May 2014 - 19:19

List Question

Why does $2+{{n}\choose{1}}+{{n}\choose{2}}+\ldots+{{n}\choose{n-1}}=(1+1)^n$

$\sum_{p\le x} \frac{1}{pq}$

Trigonometric identity involving sum of "Dirichlet kernel like" fractions

How to solve equation $\sum a_i/(x + b_i)=1$?

Are these two summations equivalent?

How find the sum $2\sum_{k=1}^{\infty}\sum_{i=0}^{2k-1}\frac{\binom{2k}{i}\cdot B_{i}\cdot(m-1)^{2k-i}}{2k(2k-1)m^{2k-1}}$

How can I define $e^x$ as the value of infinite series?

Sum with natural log

Finite Trigonometric Sum

Show $ \frac {a^3}{a^2+b^2+c^2-bc}+\frac {b^3}{a^2+b^2+c^2-ca} +\frac {c^3}{a^2+b^2+c^2-ab} \le \frac {(a+b+c)^2 (a^4+b^4+c^4)}{6abc(ab+bc+ca)} $

Convergence of $\sum_{n=1}^\infty{\frac{sin(5n)}{5^n}}$

summation of infinite series

Problem finding explicit function without multiple $\sum$s

I have the pattern: 1 + 2 + 3 + 4 + 5 + 6, but I need the formula for it

Help me with this sum: $\sum_{i=0}^\infty \frac{n}{\log^2\left(\frac{n}{5^i}\right)}$

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