How do you know when to use the Root Test for convergence of a series?

1 Answer
Nov 25, 2014

I would use Root Test when the terms of the series are in the form of some expression to the nth power; otherwise, I would try other tests first.


Let us look at examine the convergence of the series:


By Root Test,

#lim_{n to infty}root{n}{|({2n}/{5-3n})^n|}=lim_{n to infty}|{2n}/{5-3n}|#

by dividing the numerator and the denominator by #n#,

#=lim_{n to infty}|{2}/{5/n-3}|=|{2}/{0-3}|=2/3<1#

Hence, the series is absolutely convergent.

I hope that this was helpful.