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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

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    You don't need an exact answer, just a bound good enough to tell you when the series converges.2012-11-16

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

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    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?2012-12-15