Question

How to find a closed form for $\sum_{i=0}^n \binom{a+i}{b+i}i$

score 67 · Answer 1 · 2026-03-26 12:36:28

67

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How to find a closed form for $\sum_{i=0}^n \binom{a+i}{b+i}i$

Published on 26 Mar 2026 - 12:36

score 1.4k · Answer 2 · 2019-03-03 23:44:04

1.4k

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How can I write this as a double sum?

Published on 03 Mar 2019 - 23:44

score 48 · Answer 3 · 2019-03-04 02:28:45

48

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Why is the accepted summation multiplication formula what it is?

Published on 04 Mar 2019 - 2:28

score 556 · Answer 4 · 2026-03-25 22:06:20

556

Views

Bernoulli numbers in the general series-expansion formula for sums of powers?

Published on 25 Mar 2026 - 22:06

score 101 · Answer 5 · 2019-03-05 04:45:01

101

Views

Utilizing Jensen's to prove an inequality

Published on 05 Mar 2019 - 4:45

score 317 · Answer 6 · 2026-03-25 06:06:31

317

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Sums with gcd $\sum_{n=1}^{1009} \gcd(2n, 2020) - \sum_{n=0}^{1008} \gcd(2n+1, 2019)$

Published on 25 Mar 2026 - 6:06

score 95 · Answer 7 · 2026-03-25 14:28:52

95

Views

Formula for this diminishing function

Published on 25 Mar 2026 - 14:28

score 60 · Answer 8 · 2019-03-05 13:12:22

60

Views

why does this inequality regarding intersection of probabilities hold?

Published on 05 Mar 2019 - 13:12

score 115 · Answer 9 · 2026-04-02 11:09:47

115

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Correct denotation for sum function

Published on 02 Apr 2026 - 11:09

score 81 · Answer 10 · 2026-03-28 22:28:15

81

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Find all non-negative real numbers $a_1$ $\le$ $a_2$ $\le$ $\ldots$ $\le$ $a_n$

Published on 28 Mar 2026 - 22:28

score 651 · Answer 11 · 2026-03-26 11:01:17

651

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Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

Published on 26 Mar 2026 - 11:01

score 129 · Answer 12 · 2019-03-06 12:12:37

129

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Proof idea for sum of square / square of sum inequality

Published on 06 Mar 2019 - 12:12

score 64 · Answer 13 · 2026-03-25 07:45:56

64

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How to show that the $\sum_{i=1}^{n}|A[i]-x|$ is minimal for $x=m$ with median $m$?

Published on 25 Mar 2026 - 7:45

score 37 · Answer 14 · 2019-03-06 14:17:47

Evaluate sum $\sum_{k=0}^N \binom{N}{k} \prod_{j=1}^k [ (j-1)\lambda + (N-1)\mu ] \prod_{i=1}^{N-k} [(i-1)\lambda + (N-1)\gamma ]$

score 35 · Answer 15 · 2019-03-06 14:34:55

35

Views

Reformulating a sum

Published on 06 Mar 2019 - 14:34

List Question

How to find a closed form for $\sum_{i=0}^n \binom{a+i}{b+i}i$

How can I write this as a double sum?

Why is the accepted summation multiplication formula what it is?

Bernoulli numbers in the general series-expansion formula for sums of powers?

Utilizing Jensen's to prove an inequality

Sums with gcd $\sum_{n=1}^{1009} \gcd(2n, 2020) - \sum_{n=0}^{1008} \gcd(2n+1, 2019)$

Formula for this diminishing function

why does this inequality regarding intersection of probabilities hold?

Correct denotation for sum function

Find all non-negative real numbers $a_1$ $\le$ $a_2$ $\le$ $\ldots$ $\le$ $a_n$

Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

Proof idea for sum of square / square of sum inequality

How to show that the $\sum_{i=1}^{n}|A[i]-x|$ is minimal for $x=m$ with median $m$?

Evaluate sum $\sum_{k=0}^N \binom{N}{k} \prod_{j=1}^k [ (j-1)\lambda + (N-1)\mu ] \prod_{i=1}^{N-k} [(i-1)\lambda + (N-1)\gamma ]$

Reformulating a sum

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