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

The first four terms of the series probably refer to the first four partial sums.






which you can compute either by adding one term at a time, or using the well-known formula,



(I can provide a link to a derivation I gave in a nearly identical question in the comments)

The series converges as if and only if , which is certainly the case here, since .

Extrapolating from the formula above, the sum of the convergent series is



so the sum for this series is .