Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Consider the power series $\sum_{n\ge1} a_n z^n$ where $a_n =$ number of divisors of $n^{50}$. then the radius of convergence of $\sum_{n\ge1} a_n z^n$ is

(1) 1

(2) 50

(3) $\frac 1 {50}$

(4) 0

share|cite|improve this question
3  
So, what do you know about the number of divisors of $n^{50}$? – Gerry Myerson Nov 16 '12 at 4:26
    
@Gerry, I see your point. – Will Jagy Nov 16 '12 at 4:47
    
@Gerry if n is prime then the number of divisors of n^50 is 51, but when n is composite..? – amritha Nov 16 '12 at 5:39
1  
You don't need an exact answer, just a bound good enough to tell you when the series converges. – Gerry Myerson Nov 16 '12 at 11:05

Hint: what is the radius of convergence of $\sum_{n\ge1}z^n$? of $\sum_{n\ge1}n^{50}z^n$?

share|cite|improve this answer
    
@ Gerry 1 is the radius of convergence of ∑n≥1zn – amritha Dec 15 '12 at 20:07
    
Yes, the radius of convergence of $\sum_{n\ge1}z^n$ is $1$. Can you work out the radius of convergence of the other sum I mention? maybe using the ratio test? – Gerry Myerson Dec 15 '12 at 23:41

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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