What is the ratio between the infinite geometric series 1/3 + 1/4 + 3/16 + 9/64 + 27/256

Question

I have to find the sum of the infinite geometirc series, if it exists, but in order to do that I need to know the ratio between each of the fractions. Thanks for helping! :)

Answer 1

The infinite geometric series is 1 / 3 + 1 / 4  +  3 / 16  + 9 / 64 + 27 / 256

First term ( a ) =  1 / 3

Common ratio ( r ) = 2nd term / 1st term

Common ratio ( r ) =  (1/4) / (1/3) = 3/4 

The infinite geometric series =

.

The sum of the infinite geometric series is 4/3.