💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 17 Easy Difficulty

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

Answer

Convergent

More Answers

Discussion

You must be signed in to discuss.

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.