Sum of series 1 plus x2 plus x4.....plus xn?

Answer 1

(xn+2-1)/(x2-1)

Explanation

Let Y=1+x2+x4+...+xn. Now notice that:

Y=1+x2+x4+...+xn=x2(1+x2+x4+...+xn-2)+1

Y+xn+2=x2(1+x2+x4+...+xn-2+xn)+1

Y+xn+2=x2*Y+1

Y+xn+2-x2*Y=1

Y-x2*Y=1-xn+2

Y(1-x2)=1-xn+2

Y=(1-xn+2)/(1-x2)=(xn+2-1)/(x2-1)