I think s = x2-x2x-1
- Shaswata Roy I guess it is wrong.
Find the summation
s=x+x2+x4+x8.......till infinity
    s=x+x2+x4+x8.......∞
=>s= x(1+x2+x4+x8...∞)
=>s=x(1+s)
=>s=x1-x
IF X<1,
THEN S=1+X;
IF X≥1 ,
THEN S=∞
IF X<0 ,
THEN S=1-X;
Hint: Concentrate on 2nd,3rd,4th terms leaving aside the 1st term.... :)
This is a Lacunary function [See-"http://en.wikipedia.org/wiki/Lacunary_function"].
It does not have a closed form.