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Section 4-6 : Integral Test

1. Determine if the following series converges or diverges

\[\sum\limits_{n = 1}^\infty {\frac{1}{{{n^\pi }}}} \] Show Solution

There really isn’t all that much to this problem. We could use the Integral Test on this series or we could just use the \(p\)-series Test we discussed in the notes for this section.

We can clearly see that \(p = \pi > 1\) and so by the \(p\)-series Test this series must converge.