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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
Prove that : `C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+….+C_(n)^(2)=""^(2n)C_(n)`

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