Question

Combinations and Summations" $\sum_{x=0}^{n/k} \binom n{kx}$

score 121 · Answer 1 · 2026-04-15 13:39:48

121

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Combinations and Summations" $\sum_{x=0}^{n/k} \binom n{kx}$

Published on 15 Apr 2026 - 13:39

score 1.6k · Answer 2 · 2026-04-28 12:21:32

1.6k

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Double index summation: $\sum_{ 1 \leq i < j \leq 3 }(2i+j). $

Published on 28 Apr 2026 - 12:21

score 175 · Answer 3 · 2026-04-16 14:02:29

175

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$\sum_{i=0}^{\lfloor\frac{n}{k}\rfloor}{n \choose i * k}$ in a closed form

Published on 16 Apr 2026 - 14:02

score 379 · Answer 4 · 2026-04-13 22:41:55

379

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Half of sum of any two relatively prime numbers will be relatively prime to half of their difference. How will I prove it?

Published on 13 Apr 2026 - 22:41

score 239 · Answer 5 · 2026-04-12 08:40:23

239

Views

Integral involving a dilogarithm versus an Euler sum.

Published on 12 Apr 2026 - 8:40

score 421 · Answer 6 · 2026-04-12 01:39:52

421

Views

A Geometric sequence question I find confusing; should I start from $a_1=1000$ or $a_1=250$? And why?

Published on 12 Apr 2026 - 1:39

score 910 · Answer 7 · 2026-04-13 12:34:00

910

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How to use induction to show the lower bound of this function?

Published on 13 Apr 2026 - 12:34

score 169 · Answer 8 · 2026-04-17 08:32:57

169

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How many unique sums $x_0+x_1+x_2+\cdots+x_n=S$ where $x_i>x_{i-1}$?

Published on 17 Apr 2026 - 8:32

score 445 · Answer 9 · 2026-04-10 10:54:14

445

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Generating function for cubes of Harmonic numbers

Published on 10 Apr 2026 - 10:54

score 28 · Answer 10 · 2026-04-14 02:48:33

28

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Where was my reasoning off in evaluating the expectation value of $x$ in this Gaussian distribution?

Published on 14 Apr 2026 - 2:48

score 161 · Answer 11 · 2026-04-14 02:34:00

161

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Finding an Expression for $\sum_{i=1}^{n}{\frac{i}{(i+1)!}}$

Published on 14 Apr 2026 - 2:34

score 6.6k · Answer 12 · 2026-04-15 07:34:18

6.6k

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Find $\sum_{r=2}^{100}\frac{3^r(2-2r)}{(r+1)(r+2)}$

Published on 15 Apr 2026 - 7:34

score 62 · Answer 13 · 2026-04-16 12:58:47

62

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$3(1-3x)^{-2}=\sum_{n=0}^{\infty}(n+1)3^nx^n.$ How?

Published on 16 Apr 2026 - 12:58

score 1.4k · Answer 14 · 2026-04-15 18:37:32

1.4k

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Evaluate $\sum\limits_{k=0}^n(-1)^{n+k}{n\choose k}{ {n+k}\choose n} \frac{1}{k+2}$

Published on 15 Apr 2026 - 18:37

score 733 · Answer 15 · 2026-04-26 19:31:22

733

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Relative error of machine summation

Published on 26 Apr 2026 - 19:31

List Question

Combinations and Summations" $\sum_{x=0}^{n/k} \binom n{kx}$

Double index summation: $\sum_{ 1 \leq i < j \leq 3 }(2i+j). $

$\sum_{i=0}^{\lfloor\frac{n}{k}\rfloor}{n \choose i * k}$ in a closed form

Half of sum of any two relatively prime numbers will be relatively prime to half of their difference. How will I prove it?

Integral involving a dilogarithm versus an Euler sum.

A Geometric sequence question I find confusing; should I start from $a_1=1000$ or $a_1=250$? And why?

How to use induction to show the lower bound of this function?

How many unique sums $x_0+x_1+x_2+\cdots+x_n=S$ where $x_i>x_{i-1}$?

Generating function for cubes of Harmonic numbers

Where was my reasoning off in evaluating the expectation value of $x$ in this Gaussian distribution?

Finding an Expression for $\sum_{i=1}^{n}{\frac{i}{(i+1)!}}$

Find $\sum_{r=2}^{100}\frac{3^r(2-2r)}{(r+1)(r+2)}$

$3(1-3x)^{-2}=\sum_{n=0}^{\infty}(n+1)3^nx^n.$ How?

Evaluate $\sum\limits_{k=0}^n(-1)^{n+k}{n\choose k}{ {n+k}\choose n} \frac{1}{k+2}$

Relative error of machine summation

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