Question

Prove $1 + \sum_{i=0}^n(\frac1{x_i}\prod_{j\neq i}(1+\frac1{x_j-x_i}))=\prod_{i=0}^n(1+\frac1{x_i})$

score 219 · Answer 1 · 2013-09-21 06:14:55

219

Views

Prove $1 + \sum_{i=0}^n(\frac1{x_i}\prod_{j\neq i}(1+\frac1{x_j-x_i}))=\prod_{i=0}^n(1+\frac1{x_i})$

Published on 21 Sep 2013 - 6:14

score 952 · Answer 2 · 2013-09-28 00:02:41

952

Views

Summation of a product

Published on 28 Sep 2013 - 0:02

score 3.3k · Answer 3 · 2013-09-28 14:23:17

3.3k

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Check if this proof about real numbers with an irrational product is correct.

Published on 28 Sep 2013 - 14:23

score 416 · Answer 4 · 2013-09-30 00:33:59

416

Views

Why does $\frac{d}{d\theta} \left(\theta \ln\prod\limits_{i=1}^nx_i\right) = \sum\limits_{i=1}^n\ln x_i$

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score 2.1k · Answer 5 · 2026-03-29 03:53:23

2.1k

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score 20.3k · Answer 6 · 2013-10-03 19:54:09

20.3k

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score 267 · Answer 7 · 2013-10-05 19:04:07

267

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score 784 · Answer 8 · 2013-10-10 18:12:14

784

Views

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score 787 · Answer 9 · 2013-10-11 11:08:01

787

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score 120 · Answer 10 · 2013-10-13 10:46:59

120

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score 38 · Answer 11 · 2013-10-15 23:07:38

38

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Published on 15 Oct 2013 - 23:07

score 25 · Answer 12 · 2013-10-18 16:42:12

25

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score 53 · Answer 13 · 2013-10-18 19:26:05

53

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score 94 · Answer 14 · 2026-03-29 05:43:08

94

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score 61 · Answer 15 · 2013-10-21 19:07:23

61

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List Question

Prove $1 + \sum_{i=0}^n(\frac1{x_i}\prod_{j\neq i}(1+\frac1{x_j-x_i}))=\prod_{i=0}^n(1+\frac1{x_i})$

Summation of a product

Check if this proof about real numbers with an irrational product is correct.

Why does $\frac{d}{d\theta} \left(\theta \ln\prod\limits_{i=1}^nx_i\right) = \sum\limits_{i=1}^n\ln x_i$

Dot product of the column vectors from a matrix and their transposes through matrix multiplication

Can the limit of a product exist if neither of its factors exist?

$\textbf{C}$-Monoids and products

How would one discover this finite product identity?

Conditional expected value of a product of two independent normal variables

How to simplify the product of $(x^{2^k}+x^{-2^k})$ over $k$?

Is there a fast way to compute coefficient of some term of the product of some series'?

Validity of an inequality

Curiosity in a product

Trigonometry and complex numbers

Proving the convergence of a product

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