`""^(n+1)C_(2)+2(""^(2)C_(2)+""^(3)C_(2)+""^(4)C_(2)+....+""^(n)C_(2))` का मान है

If nge2 , ^(n+1)C_(2)+2(.^2C_(2)+^(3)C_(2)+^(4)C_(2)+...+^(n)C_(2))=

The value of sum (""^(n) C_(1) )^(2)+ (""^(n) C_(2) )^(2) + (""^(n) C_(3))^(2) + …+ (""^(n) C_(n) )^(2) is

Prove that : ""^(n)C_(0).""^(2n)C_(n)-""^(n)C_(1).""^(2n-2)Cn_(n)+""^(n)C_(2).""^(2n-4)Cn_(n)+......=2^n

Prove that (""^(2n)C_(0))^2-(""^(2n)C_(1))^2+(""^(2n)C_(2))^2-.....+(-1)^n(""^(2n)C_(2n))^2=(-1)^n.""^(2n)C_(n)

Prove that (""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))^(2)-…+(""^(2n)C_(2n))^(2)=(-1)^(n)*""^(2n)C_(n) .

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)=

C_(0)^(2)+3*C_(1)^(2)+5*C_(2)^(2)+.........+(2n+1)*C_(n )^(2)=

Prove the equality 1^(2)+2^(2)+3^(2) . . .+n^(2)=.^(n+1)C_(2)+2(.^(n)C_(2)+.^(n-1)C_(2) . . .+.^(2)C_(2)) .

If ""^(2n)C_(1), ""^(2n)C_(2) and ""^(2n)C_(3) are in A.P., find n.