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Problem 26 Easy Difficulty
Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {n}{n^4 + 1} $
Answer
Convergent
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Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Samuel H.
University of Nottingham
Michael J.
Idaho State University
Joseph L.
Boston College
Watch More Solved Questions in Chapter 11
Video Transcript
for this problem really is the comparison to and over end of the fourth plus one. It's always going to be less than n over just end of the fourth, because end of the fourth plus one is greater than end of the fourth. So dividing by a larger number, build a smaller number of all but end over end of the fourth reduces to one over and cute. We know that the series one over and Cubed converges as it is a P series. So, by comparison, test if our larger limit is this convergent series or sort of our larger terms come from this convergent series. In smaller terms of what we started with, we have convergent by comparison.
Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Samuel H.
University of Nottingham
Michael J.
Idaho State University
Joseph L.
Boston College