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### Section 10.6 : 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.