Question

Computing $2 \binom{n}{0} + 2^2 \frac{\binom{n}{1}}{2} + 2^3 \frac{\binom{n}{2}}{3} + \cdots + 2^{n+1} \frac{\binom{n}{n}}{n+1}$

score 103 · Answer 1 · 2026-04-17 07:37:27

103

Views

Computing $2 \binom{n}{0} + 2^2 \frac{\binom{n}{1}}{2} + 2^3 \frac{\binom{n}{2}}{3} + \cdots + 2^{n+1} \frac{\binom{n}{n}}{n+1}$

Published on 17 Apr 2026 - 7:37

score 147 · Answer 2 · 2026-04-15 11:02:55

147

Views

Simplify $\sum^{20}_{k=10} k\binom{k-1}{9}$.

Published on 15 Apr 2026 - 11:02

score 134 · Answer 3 · 2026-04-14 20:34:22

134

Views

Unusual ways of summing well-known series -- for example, this unusual summation of the geometric series

Published on 14 Apr 2026 - 20:34

score 298 · Answer 4 · 2026-04-15 22:25:13

298

Views

About closed form or an upper bound on a summation of harmonic number

Published on 15 Apr 2026 - 22:25

score 69 · Answer 5 · 2026-04-12 21:09:42

69

Views

An equivalent condition of $f$ is integrable over $R\subseteq\mathbb{R}^2$

Published on 12 Apr 2026 - 21:09

score 74 · Answer 6 · 2026-04-13 09:49:46

74

Views

Can you find a single solution of this function?

Published on 13 Apr 2026 - 9:49

score 1.6k · Answer 7 · 2026-03-25 17:36:05

1.6k

Views

Bessel functions in terms of the confluent hypergeometric function

Published on 25 Mar 2026 - 17:36

score 94 · Answer 8 · 2026-03-26 06:20:35

94

Views

Why doesn't $\sum_{n=0}^\infty2^n=-1$?

Published on 26 Mar 2026 - 6:20

score 153 · Answer 9 · 2026-04-17 12:20:14

153

Views

Evaluating S depending upon following condition: Calculate the sum $S=\Sigma \Sigma \Sigma x_{i} x_{j} x_{k},$

Published on 17 Apr 2026 - 12:20

score 110 · Answer 10 · 2026-04-17 08:00:20

110

Views

Found bounds for a sum of binom coefficients(generalization of Vandermonde's identity)

Published on 17 Apr 2026 - 8:00

score 115 · Answer 11 · 2026-04-14 13:52:07

115

Views

Closed formula for the sum $a^1+a^4+a^9...$

Published on 14 Apr 2026 - 13:52

score 111 · Answer 12 · 2026-04-17 06:34:32

111

Views

Summation involving Gamma function

Published on 17 Apr 2026 - 6:34

score 72 · Answer 13 · 2026-04-09 18:42:07

72

Views

need to find sum of $\sum_{k=1}^n \frac{(k-1)2^k}{k(k+1)}$

Published on 09 Apr 2026 - 18:42

score 112 · Answer 14 · 2026-04-16 11:51:16

112

Views

If $p$ and $q$ are coprime positive integers s.t. $\frac{p}{q}=\sum_{k=0}^{100}\frac1{3^{2^k}+1}$, what is the smallest prime factor of $p$?

Published on 16 Apr 2026 - 11:51

score 60 · Answer 15 · 2026-04-17 07:42:47

60

Views

prove that $\binom{k+1}{1} S_k(n)+\binom{k+1}{2} S_{k-1}(n)+.........+\binom{k+1}{k+1} S_0(n)=(n+1)^{k+1}-1$

Published on 17 Apr 2026 - 7:42

List Question

Computing $2 \binom{n}{0} + 2^2 \frac{\binom{n}{1}}{2} + 2^3 \frac{\binom{n}{2}}{3} + \cdots + 2^{n+1} \frac{\binom{n}{n}}{n+1}$

Simplify $\sum^{20}_{k=10} k\binom{k-1}{9}$.

Unusual ways of summing well-known series -- for example, this unusual summation of the geometric series

About closed form or an upper bound on a summation of harmonic number

An equivalent condition of $f$ is integrable over $R\subseteq\mathbb{R}^2$

Can you find a single solution of this function?

Bessel functions in terms of the confluent hypergeometric function

Why doesn't $\sum_{n=0}^\infty2^n=-1$?

Evaluating S depending upon following condition: Calculate the sum $S=\Sigma \Sigma \Sigma x_{i} x_{j} x_{k},$

Found bounds for a sum of binom coefficients(generalization of Vandermonde's identity)

Closed formula for the sum $a^1+a^4+a^9...$

Summation involving Gamma function

need to find sum of $\sum_{k=1}^n \frac{(k-1)2^k}{k(k+1)}$

If $p$ and $q$ are coprime positive integers s.t. $\frac{p}{q}=\sum_{k=0}^{100}\frac1{3^{2^k}+1}$, what is the smallest prime factor of $p$?

prove that $\binom{k+1}{1} S_k(n)+\binom{k+1}{2} S_{k-1}(n)+.........+\binom{k+1}{k+1} S_0(n)=(n+1)^{k+1}-1$

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