((-1)^{n}e^{1/n})/n^{3}converges absolutely apparently, but I don't see how. When I applied the ratio test, it came out to be one, but obviously that is incorrect. Here is what I did: | [((-1)^{n+1 }e^{1/n+1})/(n+1)^{3}] * [n^{3}/(-1)^{n}e^{1/n}] | = | [n^{3}/(n+1)^{3}] * [e^{1/n+1}/e^{1/n}] | = 1, as n -> infinity