Question

How to prove that an alternate sum is positive? $S(p,n)=\sum _{k=0}^{n+3} (-1)^k \binom{n+2 p+4-k}{2 p+1} \binom{2 n+2 p+7}{k} (n+p+3-k)^{2 n+4}$

score 128 · Answer 1 · 2026-04-16 07:16:15

128

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How to prove that an alternate sum is positive? $S(p,n)=\sum _{k=0}^{n+3} (-1)^k \binom{n+2 p+4-k}{2 p+1} \binom{2 n+2 p+7}{k} (n+p+3-k)^{2 n+4}$

Published on 16 Apr 2026 - 7:16

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233

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List Question

How to prove that an alternate sum is positive? $S(p,n)=\sum _{k=0}^{n+3} (-1)^k \binom{n+2 p+4-k}{2 p+1} \binom{2 n+2 p+7}{k} (n+p+3-k)^{2 n+4}$

Summation of an infinite Exponential series

Trigonometric functions limit to complex infinity

Sum n, n/2, n/4, ...

Summation $\sum_{n=1}^\infty \frac{1}{2^n+1}$

Asymptotic behavior of trigonometric functions near infinity

Does the function $H_{\lfloor x \rfloor} - \log(x)$ converge?

What allows us to say that $y=g(x)$?

How to calculate $\lim\limits_{n \to \infty} nx^{n+1}$ where $x\in(-1,1)$

Directional Derivatives...

Prove $\lim_{x \to 0} \frac{1}{x^{2k}}e^{-\frac{1}{x}} = 0$ (IMPROVED, first attempt added).

Let be $f:\mathbb R \to \mathbb R$ be a function satisfying $f(x+y)=f(x).f(y)$. Which one of the following are correct?

How do I find the limit without using L'Hopitals?

Why does Partial Derivative "Fail" despite Limit Definition

How do you know a limit is towards infinity or is undefined

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