Question

Asymptotics of an almost binomial sum

score 98 · Answer 1 · 2026-04-08 12:33:08

98

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Asymptotics of an almost binomial sum

Published on 08 Apr 2026 - 12:33

score 50 · Answer 2 · 2026-04-14 03:48:24

50

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Are there methods for "recovering" a sequence $a_n$ if we are given that $\sum_{k=0}^{f(x)} a_k = x$ for all $x$?

Published on 14 Apr 2026 - 3:48

score 427 · Answer 3 · 2026-04-16 12:47:54

427

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show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

Published on 16 Apr 2026 - 12:47

score 132 · Answer 4 · 2026-03-25 22:23:48

132

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Sum of multinomial coefficients with bounded indices

Published on 25 Mar 2026 - 22:23

score 46 · Answer 5 · 2026-04-13 01:54:27

46

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"Sum" of probabilities equals infinity

Published on 13 Apr 2026 - 1:54

score 36 · Answer 6 · 2026-04-16 09:17:20

36

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Convergence of $ \begin{array}{l}\sum _{n=0}^{\infty }\frac{\left(2k^2+2k+1\right)}{k^4+2k^3+k^2}\end{array}$

Published on 16 Apr 2026 - 9:17

score 126 · Answer 7 · 2026-04-15 16:26:18

126

Views

Prove that: $1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2n+1}$ is not an Integer for any integer $n$

Published on 15 Apr 2026 - 16:26

score 142 · Answer 8 · 2026-04-15 13:01:56

142

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Show $\sum_{k=0}^{n} \binom{n}{k} \binom{r+k}{n} =\sum_{k=0}^{n} (-1)^{n-k} \binom{n}{k} \binom{r+k}{k} 2^k$?

Published on 15 Apr 2026 - 13:01

score 75 · Answer 9 · 2026-04-15 11:57:06

75

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Does $\sum _{n=1}^{\infty }\sum _{i=1}^{n }\frac{\left(-1\right)^n}{i\cdot n}$ have a finite value? If so, evaluate its closed form.

Published on 15 Apr 2026 - 11:57

score 30 · Answer 10 · 2026-04-16 08:50:52

30

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Proving that: $ \sum_{j=1}^{\log_2m}m/2^j \geq m-1 $

Published on 16 Apr 2026 - 8:50

score 57 · Answer 11 · 2026-04-15 17:40:34

57

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Does $\frac{1}{n}\sum_{k=0}^{n-1}f(k)=f(n)+\epsilon_n$ imply that $f(n)$ converges?

Published on 15 Apr 2026 - 17:40

score 71 · Answer 12 · 2026-04-11 02:28:48

71

Views

How to prove two binomial expressions are equivalent?

Published on 11 Apr 2026 - 2:28

score 145 · Answer 13 · 2026-04-26 09:36:12

145

Views

Approximate the integral $\int_0^{0.5}{x^2e^{x^2}}dx$ correct to four decimal places using a Maclaurin series.

Published on 26 Apr 2026 - 9:36

score 114 · Answer 14 · 2026-05-11 07:40:44

114

Views

Olympiad Inequality: Cauchy Schwartz

Published on 11 May 2026 - 7:40

score 165 · Answer 15 · 2026-04-12 20:45:26

165

Views

A certain sum of products of binomial coefficients

Published on 12 Apr 2026 - 20:45

List Question

Asymptotics of an almost binomial sum

Are there methods for "recovering" a sequence $a_n$ if we are given that $\sum_{k=0}^{f(x)} a_k = x$ for all $x$?

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

Sum of multinomial coefficients with bounded indices

"Sum" of probabilities equals infinity

Convergence of $ \begin{array}{l}\sum _{n=0}^{\infty }\frac{\left(2k^2+2k+1\right)}{k^4+2k^3+k^2}\end{array}$

Prove that: $1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2n+1}$ is not an Integer for any integer $n$

Show $\sum_{k=0}^{n} \binom{n}{k} \binom{r+k}{n} =\sum_{k=0}^{n} (-1)^{n-k} \binom{n}{k} \binom{r+k}{k} 2^k$?

Does $\sum _{n=1}^{\infty }\sum _{i=1}^{n }\frac{\left(-1\right)^n}{i\cdot n}$ have a finite value? If so, evaluate its closed form.

Proving that: $ \sum_{j=1}^{\log_2m}m/2^j \geq m-1 $

Does $\frac{1}{n}\sum_{k=0}^{n-1}f(k)=f(n)+\epsilon_n$ imply that $f(n)$ converges?

How to prove two binomial expressions are equivalent?

Approximate the integral $\int_0^{0.5}{x^2e^{x^2}}dx$ correct to four decimal places using a Maclaurin series.

Olympiad Inequality: Cauchy Schwartz

A certain sum of products of binomial coefficients

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