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

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

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

If a_r is the coefficient of x^r in the expansion of (1+x+x^2)^n , then a_1-2a_2 + 3a_3.....-2na_(2n)=

If a_r is the coefficient x^r in the expansion of (1+x+x^2)^n then a_1 - 2a_2 + 3a_3 -…..-2na_(2n) =

If in the expansion of (1-x)^(2n-1) a_r denotes the coefficient of x^r then prove that a_(r-1) +a_(2n-r)=0

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .