If the expression in powers of `x` of the function `1/((1-ax)(1-bx))` is `a_0+a_1 x+a_2 x^2+a_3 x^3+...` then `a_n` is

If (1+x-3x^2)^2145 = a_0+a_1 x+a_2 x^2+... then a_0-a_1+a_2-.. ends with

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_1+a_3+a_5+…

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_0,a_1,a_2,.... be the coefficients in the expansion of (1+x+x^2)^n in ascending powers of x. prove that : (i) a_0a_1-a_1a_2+a_2a_3-....=0

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 the coefficient of-four successive termsin the expansion of (1+x)^n be a_1 , a_2 , a_3 and a_4 respectivel. Show that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2 a_2/(a_2+a_3)

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).