If `(x^2+x)/(1-x)=a_1x+a_2x^2+................oo , |X| <1` then

If (1+x+2x^2)^20=a_0 + a_1x+a_2x^2+....................+a_40x^40 then a_0+a_2+a_4+.............+a_38 is

The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+..............+x^a are mutiplied together and the terms of the product thus obtained are arranged in increasing powers of x in the from of a_0+a_1x+a_2x^2+................., then,

If (1-px)^-1/((1-qx))=a_0+a_1x+a_2x^2+a_3x^3+....... then a_n=

Let f(x)=a_0+a_1x+a_2x^2+.....+a_nx^n+ ....and f(x)/(1-x)=b_0+b_1x+b_2x^2+.....+b_nx^n+ ...., then

If (1+x-2x^2)^6=1+a_1x+a_2x^(2)+.........+a_(12)x^(12), then find the value of a_2+a_4+a_6+................+a_(12) .

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+.......+a_(2n)x^(2n) , then prove that a_0+a_2+a_4+....+a_(2n)=1/2(3^n+1) .

If (1+x+x^2+x^3)^100=a_0+a_1x+a_2x^2+.......+a_300x^300, then

Given (1-2x+5x^2-10x^3)(1+x)^n=1+a_1x+a_2x^2+.... and that a_1^2=2a_2 , then the value of n is

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0+a_1+a_2+… .

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0-a_1+a_2_... .