# Math Help - series convergent or divergent?

1. ## series convergent or divergent?

Could someone help me show the convergence/divergenceof the following (without the Dirichlet test or Abel sum test)?

sum(cos(n)/n) from n=1 to inf

I cannot use the comparison test since cos(n) alternates and our prof. does not want us to use Dirichlet test. Could someone please help?

Thanks!

2. Originally Posted by sdh2106
Could someone help me show the convergence/divergenceof the following (without the Dirichlet test or Abel sum test)?

sum(cos(n)/n) from n=1 to inf

I cannot use the comparison test since cos(n) alternates and our prof. does not want us to use Dirichlet test. Could someone please help?

Thanks!
If you're doing this rigorously I would note that if $\displaystyle s_m=\sum_{n=1}^{m}\frac{\cos(n)}{n}$ then $\displaystyle s_m=\text{Re}\sum_{n=1}^{m}\frac{e^{in}}{n}$ and go from there.

3. the op asked for convergence proof, not for sum value.