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Prove that : For n = 0, 1, 2, 3, ………., n...

Prove that : For n = 0, 1, 2, 3, ………., n, prove that
`C_(0).C_(r)+C_(1).C_(r+1)+C_(2).C_(r+2)+….+C_(n-r).C_(n)`
`=""^(2n)C_((n+r))` and hence deduce that
`C_(0).C_(1)+C_(1).C_(2)+C_(2).C_(3)+……..+C_(n-1).C_(n)=""^(2n)C_(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
`=""^(2n)C_(n+1)`
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