सिध्द कीजिए कि -
`C_(0)C_(r)+C_(1)C_(r+1)+C_(2)C_(r+2)+....+C_(n-r)C_(n)=((2n)!)/((n-r)!(n+r)!)`

Show that: C_0C_r+C_1C_(r+1)+C_2C_(r+2)+….+C_(n-r)C_n= ((2n)!)/((n-r)!(n+r)!)

Prove that C_0C_r+C_1 C_(r+1)+ C_2 C_(r+2)+...............+c_(n-r) C_n=((2n)!)/((n-r)!(n+r)!)

Prove that C_0C_r+C_1 C_(r+1)+ C_2 C_(r+2)+...............+c_(n-r) C_n=((2n)!)/((n-r)!(n+r)!)

If C_0, C_1, C_2 ,……..C_n are the coefficient in the expansion of (1 + x)^n then show that C_0 C_r + C_1 C_(r + 1) + C_2 C_(r + 2) + ………..+ C_(n-r).C_n = ((2n)!)/((n-r)!(n+r)!)

C_(0)-C_(1)+C_(2)-C_(3)+......+(-1)^(r)C_(r)=((-1)^(r)(n-1)!)/(r!*(n-r-1)!)

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)

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=.^(n+2)C_(r)(2lerlen) .

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=