Perhaps I'm unusual, but I avoid the phrase "

**limit **of a

**series**"; what you are talking about are the

**sum **of the series and the

**limit **of the sequence. That was my main point: mixing the terms invites confusion.

To be honest, I hadn't noticed the OP's use of the phrase:

he also said we **need **to do a divergent test, which I didn't include because I didn't know how to calculate the **limit of the series**, any help with this too would be great

I suspect they are confused by the phrase, since the limit used in the divergence test is easy in this case.

But also, I see no need to separately do a divergence test, because comparison to a geometric series already incorporates that; if you can show by any means that a series

**converges**, then its terms

**must **converge to 0. Perhaps that is just this teacher's practice, in order to keep the divergence test on students' minds.

And, no, I don't see any way to determine (easily) the

**sum **of the series, which is not required for the problem.