Let $\sum_2^\infty a_nx^n$ be a power series. Find the radius of convergence when $\lim \limits_{n \to \infty} \frac {a_n}{3^n}$ = 1.

There are a few more questions in this manner, but I'd like to understand how to tackle a simple one with some help before I go onto the harder ones. I'm guessing the root test will be used in this.


You have

$$\lim_{n\to \infty} \sqrt[n]{a_n} = \lim_{n\to \infty} {3}\frac{1}{3}\sqrt[n]{a_n}= \lim_{n\to \infty} {3}\sqrt[n]{\frac{a_n}{3^n}} = 3$$

So, with root test for power series, $R=\frac{1}{3}$

  • $\begingroup$ Could you help me with a follow-up? Now $\lim \limits_{n \to \infty} \frac {a_n}{n^3}$ = 1. Find R $\endgroup$ – Ronique Hossain Mar 2 '15 at 21:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.