Prove-that-r-1-2n-1-1-r-1-r-2n-C-r-n-n-1-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 24010 by Tinkutara last updated on 11/Nov/17

Prove that Σ_(r=1) ^(2n−1) (−1)^(r−1) ∙(r/(^(2n) C_r )) = (n/(n + 1)) .

$$\mathrm{Prove}\:\mathrm{that}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \centerdot\frac{{r}}{\:^{\mathrm{2}{n}} {C}_{{r}} }\:=\:\frac{{n}}{{n}\:+\:\mathrm{1}}\:. \\ $$

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Prove-that-r-1-2n-1-1-r-1-r-2n-C-r-n-n-1-

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