^{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