Question

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?

score 57 · Answer 1 · 2026-04-15 05:03:49

57

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Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?

Published on 15 Apr 2026 - 5:03

score 191 · Answer 2 · 2026-04-15 22:01:23

191

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(Taylor's theorem) Proving that $\sin(x) = \sum\limits_{n=0}^{\infty}\dfrac{(-1)^{n}x^{2n+1}}{(2n+1)!}$

Published on 15 Apr 2026 - 22:01

score 107 · Answer 3 · 2026-04-14 22:15:29

107

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Einstein Summation - does the following equality hold: $a_{ij} x_i y_j = a_{ij} y_i x_j$

Published on 14 Apr 2026 - 22:15

score 62 · Answer 4 · 2026-04-09 14:25:35

62

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Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$

Published on 09 Apr 2026 - 14:25

score 198 · Answer 5 · 2026-03-25 11:01:25

198

Views

symetric inequality for a rational function of three variables

Published on 25 Mar 2026 - 11:01

score 91 · Answer 6 · 2026-04-17 07:43:20

91

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Prove that $\frac{1}{1^4}+\frac{1}{2^4}+\cdots+\frac{1}{n^4} \le 2-\frac{1}{\sqrt{n}}$

Published on 17 Apr 2026 - 7:43

score 299 · Answer 7 · 2026-04-11 14:58:50

299

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Sum of a Series to Infinity

Published on 11 Apr 2026 - 14:58

score 32 · Answer 8 · 2026-04-17 01:48:45

32

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How do I evaluate $\sum _{ i=1 }^{ 2^n } (\frac{i}{2^n} - \frac{i-1}{2^n})(1-\frac{i-1}{2^n})$

Published on 17 Apr 2026 - 1:48

score 11.6k · Answer 9 · 2026-04-16 11:49:12

11.6k

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Proof of $\cos \theta+\cos 2\theta+\cos 3\theta+\cdots+\cos n\theta=\frac{\sin\frac12n\theta}{\sin\frac12\theta}\cos\frac12(n+1)\theta$

Published on 16 Apr 2026 - 11:49

score 4.1k · Answer 10 · 2026-04-10 09:53:15

4.1k

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Sum of Squares of Harmonic Numbers

Published on 10 Apr 2026 - 9:53

score 364 · Answer 11 · 2026-04-16 21:58:01

364

Views

Proof that falling power can be converted to sum of normal powers

Published on 16 Apr 2026 - 21:58

score 731 · Answer 12 · 2026-04-16 17:09:09

731

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Probability of a minimum sum of card values when drawing cards from a custom deck

Published on 16 Apr 2026 - 17:09

score 475 · Answer 13 · 2026-04-15 15:14:17

475

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Gosper's Identity $\sum_{k=0}^n{n+k\choose k}[x^{n+1}(1-x)^k+(1-x)^{n+1}x^k]=1 $

Published on 15 Apr 2026 - 15:14

score 2.7k · Answer 14 · 2026-04-13 17:25:59

2.7k

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Using induction to prove a formula for $\sin x+\sin 3x+\dots+\sin (2n-1)x$

Published on 13 Apr 2026 - 17:25

score 7.5k · Answer 15 · 2026-04-16 12:02:16

7.5k

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Calculate exact value of and infinite sum

Published on 16 Apr 2026 - 12:02

List Question

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?

(Taylor's theorem) Proving that $\sin(x) = \sum\limits_{n=0}^{\infty}\dfrac{(-1)^{n}x^{2n+1}}{(2n+1)!}$

Einstein Summation - does the following equality hold: $a_{ij} x_i y_j = a_{ij} y_i x_j$

Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$

symetric inequality for a rational function of three variables

Prove that $\frac{1}{1^4}+\frac{1}{2^4}+\cdots+\frac{1}{n^4} \le 2-\frac{1}{\sqrt{n}}$

Sum of a Series to Infinity

How do I evaluate $\sum _{ i=1 }^{ 2^n } (\frac{i}{2^n} - \frac{i-1}{2^n})(1-\frac{i-1}{2^n})$

Proof of $\cos \theta+\cos 2\theta+\cos 3\theta+\cdots+\cos n\theta=\frac{\sin\frac12n\theta}{\sin\frac12\theta}\cos\frac12(n+1)\theta$

Sum of Squares of Harmonic Numbers

Proof that falling power can be converted to sum of normal powers

Probability of a minimum sum of card values when drawing cards from a custom deck

Gosper's Identity $\sum_{k=0}^n{n+k\choose k}[x^{n+1}(1-x)^k+(1-x)^{n+1}x^k]=1 $

Using induction to prove a formula for $\sin x+\sin 3x+\dots+\sin (2n-1)x$

Calculate exact value of and infinite sum

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