Question

How is $C_0^nC_n^{n+1}+ C_1^nC_{n-1}^{n}+C_2^nC_{n-2}^{n-1}+\dots+C_n^n C_0^{1} =2^{n-1}(n+2) ?$

score 132 · Answer 1 · 2026-03-27 01:48:09

132

Views

How is $C_0^nC_n^{n+1}+ C_1^nC_{n-1}^{n}+C_2^nC_{n-2}^{n-1}+\dots+C_n^n C_0^{1} =2^{n-1}(n+2) ?$

Published on 27 Mar 2026 - 1:48

score 124 · Answer 2 · 2026-03-27 01:48:07

124

Views

If $y=\frac25+\frac{1\cdot3}{2!}\left(\frac25\right)^2 +\frac{1\cdot3\cdot5}{3!}\left(\frac25\right)^3+\ldots$ then what is the value of $y^2+2y$?

Published on 27 Mar 2026 - 1:48

score 77 · Answer 3 · 2026-03-31 17:02:30

77

Views

Help interpret notation $\sum_{j_1+j_2+\cdots+j_m=n}a^{j_1}_1a^{j_2}_2\cdots a_m^{j_m}$

Published on 31 Mar 2026 - 17:02

score 120 · Answer 4 · 2026-03-28 01:48:45

120

Views

Prove that $\sum_{k=1}^{n} \frac{(-1)^{k-1}}{k} \binom{n}{k} = 1+\frac{1}{2}+...+\frac{1}{n}$

Published on 28 Mar 2026 - 1:48

score 54 · Answer 5 · 2018-11-03 18:59:41

How to calculate the sum : $\sum_{k=1}^{n}\frac{1^2\space5^2\space...\space(4k-3)^2}{3^2\space7^2\space...\space(4k-1)^2}$?

score 44 · Answer 6 · 2018-11-04 08:19:59

44

Views

Is this correct? Convergence of $\sum_{n=2}^\infty\frac1{\log\left(\frac{n(n+1)!}2\right)}$

Published on 04 Nov 2018 - 8:19

score 62 · Answer 7 · 2018-11-04 12:54:38

62

Views

Does $\sum^\infty_{k=1} \frac{k^3-2k-3}{k^4}$ converge?

Published on 04 Nov 2018 - 12:54

score 83 · Answer 8 · 2018-11-05 14:18:44

83

Views

sum $\vert i-j\vert^{\alpha}$

Published on 05 Nov 2018 - 14:18

score 108 · Answer 9 · 2026-03-25 23:38:35

108

Views

Determining the Prime Order of a Prime Power Factorial

Published on 25 Mar 2026 - 23:38

score 109 · Answer 10 · 2018-11-05 18:32:44

109

Views

Summation problem related to fractional part function

Published on 05 Nov 2018 - 18:32

score 103 · Answer 11 · 2026-03-27 01:47:38

103

Views

How to find the sum of the given series: $\sum_{k=0}^{\min(n ,m)} \binom{n}{k} \binom{m}{k}$?

Published on 27 Mar 2026 - 1:47

score 108 · Answer 12 · 2018-11-05 19:13:57

108

Views

Finding sum of a finite series.

Published on 05 Nov 2018 - 19:13

score 1.7k · Answer 13 · 2018-11-06 05:59:14

1.7k

Views

Double summation $\sum_{m,n=1\, m\neq n}^\infty{\frac{m^2+n^2}{mn(m^2-n^2)^2}}$

Published on 06 Nov 2018 - 5:59

score 180 · Answer 14 · 2026-03-26 21:10:13

180

Views

How to find a limit of this sequence: $\lim\limits_{n \to \infty} \sum\limits_{k=1}^n \frac{1}{\sqrt{kn}}$

Published on 26 Mar 2026 - 21:10

score 38 · Answer 15 · 2026-03-26 07:02:29

38

Views

How much a variable contributed to the result of some cost function

Published on 26 Mar 2026 - 7:02

List Question

How is $C_0^nC_n^{n+1}+ C_1^nC_{n-1}^{n}+C_2^nC_{n-2}^{n-1}+\dots+C_n^n C_0^{1} =2^{n-1}(n+2) ?$

If $y=\frac25+\frac{1\cdot3}{2!}\left(\frac25\right)^2 +\frac{1\cdot3\cdot5}{3!}\left(\frac25\right)^3+\ldots$ then what is the value of $y^2+2y$?

Help interpret notation $\sum_{j_1+j_2+\cdots+j_m=n}a^{j_1}_1a^{j_2}_2\cdots a_m^{j_m}$

Prove that $\sum_{k=1}^{n} \frac{(-1)^{k-1}}{k} \binom{n}{k} = 1+\frac{1}{2}+...+\frac{1}{n}$

How to calculate the sum : $\sum_{k=1}^{n}\frac{1^2\space5^2\space...\space(4k-3)^2}{3^2\space7^2\space...\space(4k-1)^2}$?

Is this correct? Convergence of $\sum_{n=2}^\infty\frac1{\log\left(\frac{n(n+1)!}2\right)}$

Does $\sum^\infty_{k=1} \frac{k^3-2k-3}{k^4}$ converge?

sum $\vert i-j\vert^{\alpha}$

Determining the Prime Order of a Prime Power Factorial

Summation problem related to fractional part function

How to find the sum of the given series: $\sum_{k=0}^{\min(n ,m)} \binom{n}{k} \binom{m}{k}$?

Finding sum of a finite series.

Double summation $\sum_{m,n=1\, m\neq n}^\infty{\frac{m^2+n^2}{mn(m^2-n^2)^2}}$

How to find a limit of this sequence: $\lim\limits_{n \to \infty} \sum\limits_{k=1}^n \frac{1}{\sqrt{kn}}$

How much a variable contributed to the result of some cost function

Trending Questions

Popular # Hahtags

Popular Questions