# How do you test for convergence of #Sigma (-1)^n n^(-1/n)# from #n=[1,oo)#?

The series:

is not convergent.

A necessary condition for the series to converge is that:

For this series:

so:

Consequently:

which means the series is not convergent.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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