2012/020) find(1+1/2)(1+1/2^2)(1+1/2^4)-----… product of infinite rems

(1+x)(x+x^2)(1+ x^4) ,,, (1+x^(2n) n goes to infinite and x= 1/2

multiply by (1-x) to get

(1-x)((1+x)(1+x^2)(1+ x^4) ,,, (1+x^(2^n))
=(1-x^2)(1+x^2)(1+ x^4) ... (1+x^(2^n))
= (1-x^(2^(n+1))

so (1-x)((1+x)(x+x^2)(1+ x^4) ,,, (1+x^(2^n)) = ( 1- (x^(2^(n +1))/(1-x) = 1/(1-x) as n-> infinte and |x| < 1
as x = 1/2
product = 2