Prove-that-n-C-0-n-n-C-1-n-1-n-C-2-n-2-1-n-n-C-n-2n-1-n-2n-C-n-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 22394 by Tinkutara last updated on 17/Oct/17

Prove that : ((^n C_0 )/n)−((^n C_1 )/(n+1))+((^n C_2 )/(n+2))−...+(−1)^n .((^n C_n )/(2n))=(1/(n.^(2n) C_n ))

$$\mathrm{Prove}\:\mathrm{that}\::\:\frac{\:^{{n}} {C}_{\mathrm{0}} }{{n}}−\frac{\:^{{n}} {C}_{\mathrm{1}} }{{n}+\mathrm{1}}+\frac{\:^{{n}} {C}_{\mathrm{2}} }{{n}+\mathrm{2}}−…+\left(−\mathrm{1}\right)^{{n}} .\frac{\:^{{n}} {C}_{{n}} }{\mathrm{2}{n}}=\frac{\mathrm{1}}{{n}.^{\mathrm{2}{n}} {C}_{{n}} } \\ $$

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Prove-that-n-C-0-n-n-C-1-n-1-n-C-2-n-2-1-n-n-C-n-2n-1-n-2n-C-n-

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