sum 1/2^n

S_n = (1/2)^1 + (1/2)^2 + (1/2)^3  + ........+ (1/2)^(n-1) + (1/2)^n ..... where the sum ( S_n)  can be found by:

a₁ / (1 - r) ....     where a₁ is the first term = (1/2).... and  r is the geometric ratio between terms = (1/2)

So we have

(1/2) / (1 - 1/2) =  (1/2)/ (1/2)  = 1   

And that's the sum