List questions from summation

Published on 09 Apr 2026 - 3:08

285

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Compute the double sum with binomial coefficients: $ \sum_{1\leq i,j\leq n, \ i+j\leq n }\binom{i+j}{i} x^i y^j $

Published on 17 Apr 2026 - 15:54

625

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Proof for $\log\frac{2n+1}{n+1}<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}<\log 2$

Published on 16 Apr 2026 - 10:41

51

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Multivariable calculus, inner products

Published on 11 Apr 2026 - 5:45

2.8k

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Proof that sum of power series equals exponential function?

Published on 09 Apr 2026 - 22:43

1.6k

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Confusion when applying Tensor transformation law to $\partial_{[a,v_b]}$

Published on 11 Apr 2026 - 18:26

99.6k

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Can a sum of products be split as a product of two sums?

Published on 11 Apr 2026 - 11:00

153

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Closed form for this summation

Published on 11 Apr 2026 - 2:07

31

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Probing a particular function

Published on 12 Apr 2026 - 1:40

52

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Summing powers of complex root of unities gives 0

Published on 08 Apr 2026 - 4:52

431

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The history of summations

Published on 09 Apr 2026 - 20:23

1.1k

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Solve $ \sum_{k = 1}^{ \infty} \frac{\sin 2k}{k}$

Published on 12 Apr 2026 - 23:04

250

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Proof with combinatorial argument for $\binom{n}{k+1} = \binom{n-1}k+ \binom{n-2}k +...+ \binom{k}k$

Published on 16 Apr 2026 - 14:22

791

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Finding $\sum_{k=1}^{\infty} \left[\frac{1}{2k}-\log \left(1+\frac{1}{2k}\right)\right]$

Published on 25 Mar 2026 - 12:54

53

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Arithmetic sequence problem

Published on 12 Apr 2026 - 8:44

List Question

Replace $\sum$ with $\ln$

Compute the double sum with binomial coefficients: $ \sum_{1\leq i,j\leq n, \ i+j\leq n }\binom{i+j}{i} x^i y^j $

Proof for $\log\frac{2n+1}{n+1}<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}<\log 2$

Multivariable calculus, inner products

Proof that sum of power series equals exponential function?

Confusion when applying Tensor transformation law to $\partial_{[a,v_b]}$

Can a sum of products be split as a product of two sums?

Closed form for this summation

Probing a particular function

Summing powers of complex root of unities gives 0

The history of summations

Solve $ \sum_{k = 1}^{ \infty} \frac{\sin 2k}{k}$

Proof with combinatorial argument for $\binom{n}{k+1} = \binom{n-1}k+ \binom{n-2}k +...+ \binom{k}k$

Finding $\sum_{k=1}^{\infty} \left[\frac{1}{2k}-\log \left(1+\frac{1}{2k}\right)\right]$

Arithmetic sequence problem

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