Hello!!

Hope you are doing great!!!

Given series:1/2+3/4+7/8+15/16+...........

It can be written as,

=(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+...............n

=(1-1/2)+(1-1/2^2)+(1-1/2^3)+(1-1/2^4)+..............(1-1/2^n)

taking like terms common,

=(1+1+1+...........n) - (1/2+1/2^2+1/2^3+1/2^4............)

=n - (1/2+1/2^2+1/2^3+1/2^4............)

The above series is in GP

The sum of GP can be given by the formula a(1-r^n) / 1-r

=n - 1/2(1-1/2^n) / 1-1/2

=n - (1-1/2^n)

=n - 1+1/2^n

Hope it helps you!!!

Thank you!!!