If `(x^2+x+1)/(1-x)=a_0+a_1x+a_2x^2+ ,t h e nsum_(r=1)^(50)a_r` is equal to `148` b. `146` c. `149` d. none of these

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_2+a_4+…

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+…

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

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 cosx=a_0+a_1 x+a_2x^2+... then the value of a_2 is

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_1-a_3+a_5-a_7+… .

If x_(1)=2tan^(-1)((1+x)/(1-x)),x_(2)=sin^(-1)((1-x^(2))/(1+x^(2))) where x in(0,1), then x_(1)+x_(2) is equal to 0 (b) 2 pi(c)pi pi(d) none of these

If x_(1),x_(2),...x_(20) are in H.P.and x_(1),2,x_(20) are in G.P.then sum_(r=1)^(19)x_(r)x_(r+1)=76b.80c.84d none of these

If (1+x)^n = a_0+a_1x+a_2x^2+......+a_nx^n , find the sum a_0+a_4 + a_8 + a_12 + ….. .