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# Determine whether the series is convergent or divergent.$\displaystyle \sum_{n = 1}^{\infty} \frac {1}{n^2 + 4}$

## Convergent

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

so to do this, we already have the summation notation. So we're wanting to take the integral. I mean, this is going to be the integral from one to infinity of one over x squared us for the X. This is going to be, um, evaluated when we see the anti derivative of this is the inverse tangent of acts over to We can evaluate that and we end up getting that. This is one half I'm high over to minus are pungent of one house. See that we get the same answer here so we can validate it on DSO. Since this is a finite number, it doesn't go all the way to infinity. That tells us that this is a convergent Siri's.

California Baptist University

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

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