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 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 a_r is the coefficient of x^r in the expansion of (1+x)^n then a_1/a_0 + 2.a_2/a_1 + 3.a_3/a_2 + …..+n.(a_n)/(a_(n-1)) =

If a_r is the coefficient of x^r in the expansion of (1+x)^n then a_1/a_0 + 2.a_2/a_1 + 3.a_3/a_2 + …..+n.(a_n)/(a_(n-1)) =

If a _(r) is the coefficient of x^r in the expansion of (1+ x+x^(2)) ^(n), then the value of a_(1)- 2a_(2) +3a_(3)-4a_(4)+…-2na_(2n) is -

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

If a_k is the coefficient of x^k in the expansion of (1+x+x^2)^n for k = 0, 1, 2, ......., 2n then a_1+2a_2+3a_3+...+2na_(2n)=