The co-efficient of `x^n` in `(1 + x+2x^2+ 3x^3+..+ nx^n)^2` is

The co-efficient of xx^(n-2) in (x-1)(x-2)(x-3)(x-n) is :

Let the co-efficients of x^n In (1+x)^(2n) and (1+x)^(2n-1) be P & Qrespectively, then ((P+Q)/Q)^5=

Let the co-efficients of x^(n) In (1+x)^(2n) and (1+x)^(2n-1) be P& Qrespectively,then ((P+Q)/(Q))^(5)=

If |x|<1, then the co-efficient of x^(n) in the expansion of (1+x+x^(2)+x^(3)+....)^(2) is

'Prove that the co-efficient of x^n of the expansion of (1+x)^(2n) is the double of the coefficient of x^n of the expansion of '(1+x)^(2n-1)'

Find the sum of the coefficients in the expansion of (1+2x+3x^(2)+...nx^(n))^(2)

If |x| lt 1 , then the co - efficient of x^(n) in the expansion of (1+x+x^(2)+…. )^(2) is :

if n is a positive integer,find the co-efficient of x^(n) in the expansion of ((3x-2)^(n))/((1-x)^(2))

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+....(n−1).2+n.1" also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n*1 also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .