My Math Forum Verifying analytic part in example converges

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 April 6th, 2014, 06:34 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 Verifying analytic part in example converges $\displaystyle f(z)= \frac{sin(z)}{z^4}=\frac{1}{z^3} - \frac{1}{3!z} + \frac{z}{5!}- \frac{z^3}{7!} + \frac{z^5}{9!}.....$ Would like to know how to verify that the analytic part... $\displaystyle \frac{z}{5!}- \frac{z^3}{7!} + \frac{z^5}{9!}.....$ converges. Thanks!
 April 7th, 2014, 03:53 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 The proof is a small variation on the proof that the series for sin(z) converges.

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