# sum geometric series

posted by
**david**
.

what is the sum of geometric infinite series 3/2+ 9/16+ 27/128+ 81/1024=....

i know the formula is S=a/(1-r)

my teacher, he usually transforms into a formula of the sum series and finds out a and r.but i don't how to do that.

the pattern i saw is 3/2 + 3^2/2^4 + 3^3/2^7+ 3^4/2^10+....

a= 3/2 r= 3/8

3/2 + 3/2*3/8 + 3/2*3/8*3/8 + ....