Problem
Examine the following Cauchy product and the factors for convergence and in the case of convergence determine the limit.
$$\left(3 + \sum^{\infty}_{k=1}3^k\right)\left(-2+\sum^{\infty}_{k=1}2^k\right)$$
My Answer
The two factors $(3+\sum3^k)$ and $(-2+\sum 2^k)$ diverges (by for example the fact that the limit of the summand is clearly not $0$). And similarly, the whole product diverges as well (since both factors diverges to positive infinity).
Edit: I just checked Wolfram Alpha and it confirms all my answers. Maybe the question itself is just silly.
I think I'm just confused because I don't think the supposed answer should be this simple. Am I missing something?