Question

Proof of formula $\sum_{i=1}^n {}_{i+k}P_{k+1} = \sum_{i=1}^n \prod_{j=0}^k (i+j) = \frac{(n+k+1)!}{(n-1)!(k+2)}$

score 30 · Answer 1 · 2026-04-14 23:19:02

30

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Proof of formula $\sum_{i=1}^n {}_{i+k}P_{k+1} = \sum_{i=1}^n \prod_{j=0}^k (i+j) = \frac{(n+k+1)!}{(n-1)!(k+2)}$

Published on 14 Apr 2026 - 23:19

score 96 · Answer 2 · 2026-03-27 11:24:43

96

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Summation using several roots

Published on 27 Mar 2026 - 11:24

score 367 · Answer 3 · 2026-03-31 00:06:44

367

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Find the sum of series: $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{97}+\sqrt{98}}+\frac{1}{\sqrt{99}+\sqrt{100}}$

Published on 31 Mar 2026 - 0:06

score 127 · Answer 4 · 2026-04-16 11:49:54

127

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$\sum_{k=0}^{n} \frac{n!}{k!} n^k=\sum_{k=0}^{n} \binom{n}{k} k^k (n-k)^{n-k}=\sum_{k=0}^{n} \binom{n}{k} (n+k)^k (-k)^{n-k}$.

Published on 16 Apr 2026 - 11:49

score 205 · Answer 5 · 2026-03-27 11:24:42

205

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score 51 · Answer 6 · 2026-04-10 10:40:51

51

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score 551 · Answer 7 · 2026-04-16 13:55:07

551

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score 45 · Answer 8 · 2026-04-13 15:32:54

45

Views

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score 166 · Answer 9 · 2026-04-13 22:07:44

166

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score 44 · Answer 10 · 2026-04-16 03:42:52

44

Views

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Published on 16 Apr 2026 - 3:42

score 36 · Answer 11 · 2026-04-12 08:50:42

36

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score 91 · Answer 12 · 2026-04-12 04:00:13

91

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score 44 · Answer 13 · 2026-04-09 07:52:02

44

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determining a prime factorization

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score 503 · Answer 14 · 2026-04-12 23:35:06

503

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Indexing twice for conditional summation

Published on 12 Apr 2026 - 23:35

score 521 · Answer 15 · 2026-03-26 21:25:52

521

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What is the finite sum of sinc functions?

Published on 26 Mar 2026 - 21:25

List Question

Proof of formula $\sum_{i=1}^n {}_{i+k}P_{k+1} = \sum_{i=1}^n \prod_{j=0}^k (i+j) = \frac{(n+k+1)!}{(n-1)!(k+2)}$

Summation using several roots

Find the sum of series: $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{97}+\sqrt{98}}+\frac{1}{\sqrt{99}+\sqrt{100}}$

$\sum_{k=0}^{n} \frac{n!}{k!} n^k=\sum_{k=0}^{n} \binom{n}{k} k^k (n-k)^{n-k}=\sum_{k=0}^{n} \binom{n}{k} (n+k)^k (-k)^{n-k}$.

Partial Circular Sum of a Rational Function

Logarithm inequality with partial sum

Expressing the sum of all elements of a n x n matrix above the main diagonal (including)

How to determine the number of terms of a summation for a given expression

Sum of all powers of imaginary unit $\pmb i$

Cannot find recursive expression for $p_k$, when $p_{k+2}-p_k = λ(p_k-p_{k-1})$

Calc Problem with Expressing A Sum with Natural Log

Differentiating summations

determining a prime factorization

Indexing twice for conditional summation

What is the finite sum of sinc functions?

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