Consider the infinite geometric series

Question

infinity
E -4(1/3)^n-1
n=1

In this image the lower limit of the summation notion is “n-1”
a. write the first four terms of the series
b. does the series diverse or converge
c. if the series has a sum, find the sum

PLEASE SHOW YOUR WORK

Answer 1

just plug and chug ...
-4(1/3)^0 , -4(1/3)^1 , -4(1/3)^2 , -4(1/3)^3
This is just a geometric series with
a = -4
r = 1/2
So, it converges, with the sum
S = -4/(1 - 1/3) = -6