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Question

Prove that the sum of the series C1C0+2C2C1+3C3C2+....+nCnCn1=n(n+1)2.

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Solution

C1C0=n1=n=C2C1=2n(n1)2n=(n1)nCnCn1=1n×n=1

n+1(n1)++1= sum of n consequent time integers

=n(n+1)2

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