Please I need the answer in word not hand written Prove that

Please I need the answer in word not hand written

Prove that 1 + 1 / 2 + 1 / 4 + 1 / 2n - 1 = 2(1 - 1 / 2n) for all natural numbers n.

Solution

Given series 1 + 1/2 + 1/4 .............+1/(2)^n-1 is a geometric series with

a=1 ,r= 1/2, n=n

sum = a(1-r^n)/(1-r)= 1(1-(1/2)^n)/(1-1/2)=(1-1/2^n)/(1/2)=2(1-1/2^n)