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Numerade Educator

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Problem 9 Easy Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {1}{n^{\sqrt 2}} $

Answer

The series is convergent

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Video Transcript

to determine whether the Siri's is conversion, not virgin. We can use the P Siri's test, which states that for a Siri's from an equals one to infinity of the form one over end the P power in the serious converges if P is greater than one. So we noticed in this case we have won over and to the square two. So you know, he is the square root of two. And we know that the square root of two has to be greater than the squared of one. And we know that squared of one is one. So in this case, we have p greater than one, meaning the serious his conversion.