Question

On summation $\sum_{k = 0}^n \binom nk^2 x^k y^{n-k} $

score 103 · Answer 1 · 2026-04-18 11:40:03

103

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On summation $\sum_{k = 0}^n \binom nk^2 x^k y^{n-k} $

Published on 18 Apr 2026 - 11:40

score 71 · Answer 2 · 2026-04-10 09:04:54

71

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Summation of gamma function in terms of reimann zeta function

Published on 10 Apr 2026 - 9:04

score 73 · Answer 3 · 2026-04-17 12:40:22

73

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Can we rewrite a sum product without the summation notation?

Published on 17 Apr 2026 - 12:40

score 22 · Answer 4 · 2026-04-13 22:21:15

22

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Find minimum integer such that any integer \in [1, n] can be constructed from its consequent subsums

Published on 13 Apr 2026 - 22:21

score 52 · Answer 5 · 2026-04-16 14:23:39

52

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Sums of subsequences of Tribonacci number

Published on 16 Apr 2026 - 14:23

score 181 · Answer 6 · 2026-04-15 14:27:51

181

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How many different combinations of non-negative integers $i, j$ can give the same value for $n\left(i+j\right)+j$?

Published on 15 Apr 2026 - 14:27

score 293 · Answer 7 · 2026-04-14 03:55:42

293

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

Published on 14 Apr 2026 - 3:55

score 54 · Answer 8 · 2026-04-17 03:19:54

54

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If $\sum_{0}^{2n}a_r(x-2)^r=\sum_{0}^{2n}b_r(x-3)^r$ and $a_k=1$ $\forall$ $k\ge n$, then show that $b_n=\displaystyle{2n+1\choose n+1}$

Published on 17 Apr 2026 - 3:19

score 114 · Answer 9 · 2026-04-11 09:05:48

114

Views

How to find that limit by mathematica?

Published on 11 Apr 2026 - 9:05

score 249 · Answer 10 · 2026-04-10 20:28:49

249

Views

Simplifying Repeated Infinite Summation

Published on 10 Apr 2026 - 20:28

score 732 · Answer 11 · 2026-03-26 06:20:19

732

Views

A combinatorial identity - Hockey Stick generalization

Published on 26 Mar 2026 - 6:20

score 29 · Answer 12 · 2026-04-11 09:54:41

29

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Twice the product of the terms gone from summand.

Published on 11 Apr 2026 - 9:54

score 66 · Answer 13 · 2026-04-15 21:58:30

66

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Sums of subsequences of the Fibonacci numbers

Published on 15 Apr 2026 - 21:58

score 521 · Answer 14 · 2026-04-16 02:45:30

521

Views

Prove that $\sum_{i=1}^n\frac{x_i}{\sqrt[nr]{x_i^{nr}+(n^{nr}-1)\prod_{j=1}^nx^r_j}} \ge 1$ for all $x_i>0$ and $r \geq \frac{1}{n}$.

Published on 16 Apr 2026 - 2:45

score 64 · Answer 15 · 2026-04-16 10:43:32

64

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Summation question concerning the formula $P(\cup^n_{k=1}A_k) = \sum^n_{k=1}(-1)^{k-1}p_k$

Published on 16 Apr 2026 - 10:43

List Question

On summation $\sum_{k = 0}^n \binom nk^2 x^k y^{n-k} $

Summation of gamma function in terms of reimann zeta function

Can we rewrite a sum product without the summation notation?

Find minimum integer such that any integer \in [1, n] can be constructed from its consequent subsums

Sums of subsequences of Tribonacci number

How many different combinations of non-negative integers $i, j$ can give the same value for $n\left(i+j\right)+j$?

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

If $\sum_{0}^{2n}a_r(x-2)^r=\sum_{0}^{2n}b_r(x-3)^r$ and $a_k=1$ $\forall$ $k\ge n$, then show that $b_n=\displaystyle{2n+1\choose n+1}$

How to find that limit by mathematica?

Simplifying Repeated Infinite Summation

A combinatorial identity - Hockey Stick generalization

Twice the product of the terms gone from summand.

Sums of subsequences of the Fibonacci numbers

Prove that $\sum_{i=1}^n\frac{x_i}{\sqrt[nr]{x_i^{nr}+(n^{nr}-1)\prod_{j=1}^nx^r_j}} \ge 1$ for all $x_i>0$ and $r \geq \frac{1}{n}$.

Summation question concerning the formula $P(\cup^n_{k=1}A_k) = \sum^n_{k=1}(-1)^{k-1}p_k$

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