Find the sum of the following geometric series: `a/(1+i)+a/((1+i)^2)+a/((1+i)^3)+..+a/((1+i)^n)dot`

Explanation

Given,Common Ratio` = r = (a/((1+i)^2))/(a/(1+i))= 1 + i `

∴ Sum of GP for n terms =`(a(r^n−1))/(r−1) ...... (1)`

` ⇒ a = a/(1+i) , r = 1 + i, n = n `

∴ Substituting the above values in (1) we get

=`[a/(1+i)((1+i)^n-1)]/(1+i-1)`

=`(a((1+i)^n-1))/(i-1)`