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# Determine the convergence of the series (-1)n / n1/n

Consider the series

Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.

The given series diverges.

Proof. The series diverges since the limit

(Since the limit of the even terms is 1 and the limit of the odd terms is

### One comment

1. N says:

Why are you considering the (-1)^{n} when taking the limit? Shouldn’t you just consider a_n=\cfrac {1}{n^{\cfrac{1}{n}}}?