Home
Class 12
MATHS
If nge2 , ^(n+1)C(2)+2(.^2C(2)+^(3)C(2)+...

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

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

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 C_(0) , C_(1) , C_(2) ,…, C_(n) are coefficients in the binomial expansion of (1 + x)^(n) and n is even , then C_(0)^(2)-C_(1)^(2)+C_(2)^(2)+C_(3)^(2)+...+ (-1)^(n)C_(n)""^(2) is equal to .

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)= .

The value of |111^(n)C_(1)^(n+2)C_(1)^(n+4)C_(1)^(n)C_(2)^(n+2)C_(2)^(n+4)C_(2)| is

If (1+a)^(n)=.^(n)C_(0)+.^(n)C_(1)a+.^(n)C_(2)a^(2)+ . . +.^(n)C_(n)a^(n) , then prove that .^(n)C_(1)+2.^(n)C_(2)+3.^(n)3C_(3)+ . . .+n.^(n)C_(n)=n.2^(n-1) .

Prove that: .^(2)C_(2)+^(3)C_(2)+^(4)C_(2)+…..+^(n+1)C_(2)=1/6n(n+1)(n+2)