Originally Posted by

**ozfingwe** Hello,

I am supposed to show why the following series are convergent or divergent, but I didn't get very far with either direct comparison, root, or ratio tests:

1.

$\displaystyle \sum\limits_{n = 0}^\infty {\frac{{1}}

{{{n^2} + a^2 }}} $

I would have thought that by direct comparison I could show that (1) converges, but not sure. (2) leaves me at a complete loss, though.

2.

$\displaystyle \sum\limits_{n = 0}^\infty {n \left(\frac{{{2n+1} }}

{{{3n+1}}}\right)^n} $

any help appreciated.

thank you -

Oz.