[tex] \sum_{n=1}^{\infty} n \sin(\frac{1}{n}) [/tex](adsbygoogle = window.adsbygoogle || []).push({});

I rewrote the sum as [tex] \sum_{n=1}^{\infty} \frac{\sin(\frac{1}{n})}{\frac{1}{n}} [/tex]

Then I applied the Nth term test and used L'Hoptials rule so [tex] \lim_{n\to\infty} \frac{\cos(\frac{1}{n})\frac{-1}{n^2}}{\frac{-1}{n^2}} [/tex]

The [tex] \frac{-1}{n^2} [/tex] cancel out and the [tex] lim_{n\to\infty} \cos(\frac{1}{n}) [/tex] is 1 which by the nth term test is divergent. Is that a legitimate proof of divergence?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Series Convergence/Divergence Proofs

**Physics Forums | Science Articles, Homework Help, Discussion**