find the sum of the infinite geometric series 3 92 274 818

find the sum of the infinite geometric series: 3+ 9/2 + 27/4+ 81/8+ ...

Solution

sum of infinite geometric series is

S_n=a/(1-r)

In the given series,a=3

r= 9/2/3=3/2 which is greater then 1

And when r>1 the series is divergent and in that case sum tend to infinity