(1-2x+x^(2))^(n)

If a_(r) is the coefficient of x^(r) in (1-2x+3x^(2))^(n), then sum_(r=0)^(2n)r*a_(r)=

If (1+2 x+x^(2))^(n)=sum_(r=0)^(2 n) a_(r) x^(r) , then a_(r) =

If sum of all the coefficient of even powers in (1-x+x^(2)-x^(3)....x^(2n))(1+x^()+x^(2)....+x^(2n)) is 61 then n is equal to

The middle term in the expansion of (1+(1)/(x^(2)))^(n) ( 1+x^(2))^(n) is

The middle term in the expansion of (1+(1)/(x^(2)))^n ( 1+x^(2))^(n) is

Expand (1+ 2 x + 3x^(2) )^(n) in a series of ascending powers of x up to and including the term in x^2 .

lim_(x rarr1)((1-x)(1-x^(2))............(1-x^(2n)))/({(1-x)(1-x^(2)).........(1-x^(n))}^(2))

Find the sum of the series (1+2x+3x^(2)+(n-1)x^(n-2)) using differentiation.