Find the sum of the infinite geometric series 1 13 19 127

Find the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 ... 1 + 1/3 + 1/9 + 1/27 ... = (Simplify your answer)

Solution

1 + 1/3 + 1/9 + 1/27 + ....

applying sum of geometric series formula

sum = a / 1 - r

a = first term

r = common ratio

r = 1/3 / 1 = 1/3

hence ,

sum = 1 / 1 - 1/3

= 3 / 2

sum = 3/2