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Einstein summation convention differential

score 4.1k · Answer 1 · 2026-04-17 05:25:44

4.1k

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Einstein summation convention differential

Published on 17 Apr 2026 - 5:25

score 360 · Answer 2 · 2026-04-13 12:43:30

360

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Solve easy sums with Binomial Coefficient

Published on 13 Apr 2026 - 12:43

score 210 · Answer 3 · 2026-04-14 18:02:37

210

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Find a formula for the sum of the $n$ terms of the sequence (Summations & Sequences)

Published on 14 Apr 2026 - 18:02

score 244 · Answer 4 · 2026-04-11 20:34:50

244

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Why are infinite sums so much harder to calculate than the associated infinite integral?

Published on 11 Apr 2026 - 20:34

score 81 · Answer 5 · 2026-04-15 16:04:45

81

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Prove $\sum_{k=0}^{n-1}\frac{n(-1)^{n-k+1}}{n-k}{n-1 \choose k} = 1$

Published on 15 Apr 2026 - 16:04

score 281 · Answer 6 · 2026-04-14 00:41:01

281

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Combinational meaning of $\sum\limits_{k=r}^{n} {k \choose r }={{n+1} \choose r+1}$

Published on 14 Apr 2026 - 0:41

score 140 · Answer 7 · 2026-04-16 03:17:08

140

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How to prove $ 1^3+2^3+... +n^3 = (1 + 2+ \dots +n)^2 $ by induction?

Published on 16 Apr 2026 - 3:17

score 99 · Answer 8 · 2026-04-14 23:30:17

99

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Is there a proof of $\sum_{n=0}^x {{(-1)^n(x-n+1)^x}\over{n!(x-n)!}} = 1$ using induction?

Published on 14 Apr 2026 - 23:30

score 2.1k · Answer 9 · 2026-04-15 00:22:21

2.1k

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Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$

Published on 15 Apr 2026 - 0:22

score 129 · Answer 10 · 2026-04-12 07:06:27

129

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Finding a more explicit way to express a coefficient in this summation

Published on 12 Apr 2026 - 7:06

score 551 · Answer 11 · 2026-04-16 16:38:29

551

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Unusual binomial sum: $\sum_{d=k}^{n} {d \choose k} p^{d}(1-p)^{n-d}$

Published on 16 Apr 2026 - 16:38

score 1.7k · Answer 12 · 2026-04-12 15:12:13

1.7k

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By applying term-wise differentiation and integration find the sum of the series $\sum_{k=1}^{\infty}\frac{x^k}{k}$

Published on 12 Apr 2026 - 15:12

score 523 · Answer 13 · 2026-04-14 15:28:12

523

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Prove the summation involving Stirling numbers of the first kind

Published on 14 Apr 2026 - 15:28

score 59 · Answer 14 · 2026-04-16 16:00:12

59

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Find $\sum_{i=[1,\ldots,n], j=[1,\ldots,m]: i\neq j }\frac{1}{j}$

Published on 16 Apr 2026 - 16:00

score 168 · Answer 15 · 2026-04-14 05:52:27

168

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Why is this nested sum formula true

Published on 14 Apr 2026 - 5:52

List Question

Einstein summation convention differential

Solve easy sums with Binomial Coefficient

Find a formula for the sum of the $n$ terms of the sequence (Summations & Sequences)

Why are infinite sums so much harder to calculate than the associated infinite integral?

Prove $\sum_{k=0}^{n-1}\frac{n(-1)^{n-k+1}}{n-k}{n-1 \choose k} = 1$

Combinational meaning of $\sum\limits_{k=r}^{n} {k \choose r }={{n+1} \choose r+1}$

How to prove $ 1^3+2^3+... +n^3 = (1 + 2+ \dots +n)^2 $ by induction?

Is there a proof of $\sum_{n=0}^x {{(-1)^n(x-n+1)^x}\over{n!(x-n)!}} = 1$ using induction?

Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$

Finding a more explicit way to express a coefficient in this summation

Unusual binomial sum: $\sum_{d=k}^{n} {d \choose k} p^{d}(1-p)^{n-d}$

By applying term-wise differentiation and integration find the sum of the series $\sum_{k=1}^{\infty}\frac{x^k}{k}$

Prove the summation involving Stirling numbers of the first kind

Find $\sum_{i=[1,\ldots,n], j=[1,\ldots,m]: i\neq j }\frac{1}{j}$

Why is this nested sum formula true

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