Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Help finding the radius of convergence?
Find the radius of convergence (R), and the convergence interval, for the following power series:
∞
Σ (1/n)x^n
n=0
I tried using the ratio test but can't figure out the radius of convergence
1 Answer
- kbLv 710 years agoFavourite answer
Using the ratio test,
r = lim(n→∞) |(x^(n+1)/(n+1)) / (x^n/n)|
..= lim(n→∞) |(x^(n+1)/(n+1)) * (n/x^n)|
..= |x| * lim(n→∞) n/(n+1)
..= |x| * 1
..= |x|.
So, the series is guaranteed to converge for r = |x| < 1 and diverge for |x| > 1.
==> The radius of convergence is 1.
I hope this helps!
