1- 1/2^2 -1/2^3 -…-1/2^n
=1- (1/2^2+1/2^3 +…+1/2^n)
=1- (-1/2+1/2+1/2^2+1/2^3 +…+1/2^n)
=3/2-1/2*(1-(1/2)^n)/(1-1/2)
=3/2-(1-(1/2)^n)
=1/2^n-1/2