Consider the infinite geometric series n=1 -4(1/3)^n-1. a. write the first four terms of the series b. does this series converge or diverge c. if the series has a sum, find the sum

We are given an infinite geometric series:

a. To calculate first four terms we insert 1,2,3 and 4 as values for n.

b. General form of geometric series is:

Where  is first term and r is common ratio.
Series converges if -1<r<1. Otherwise it diverges.
In our case  so this means that series converges.

c. The series will have sum onlly if it converges ( -1<r<1 ). It does so we have sum. The formula is: