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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

  • 3
    So, what do you know about the number of divisors of $n^{50}$?2012-11-16
  • 0
    @Gerry, I see your point.2012-11-16
  • 0
    @Gerry if n is prime then the number of divisors of n^50 is 51, but when n is composite..?2012-11-16
  • 1
    You don't need an exact answer, just a bound good enough to tell you when the series converges.2012-11-16

1 Answers 1