Question

Can someone please help me with this one question?

Answer 1

It's been awhile since I've worked with infinite series and partial sums, but here are my thoughts:
A. the first 4 terms:  -4, $- \frac{4}{3}$, $-\frac{4}{9}$, $- \frac{4}{27}$
B. In examining the partial sums of the series, it appears that the sequence produced has a limit and therefore the series would be convergent.
C. the limit or sum of the series looks to be -5    Below look at the sequence of partial sums:  
-4, $-5 \frac{1}{3}$, $-5 \frac{7}{9}$, $-5 \frac{25}{27}$

So you can see we're getting closer and closer to -5