How would you figure out if the series converge or diverge?

Problem 1

n=1 to infinity 3/(n+n^1/2)

Problem 2

n=1 to infinity 1+cos n/ n^2

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- Mar 22nd 2009, 03:54 PMTAG16comparison tests
How would you figure out if the series converge or diverge?

Problem 1

n=1 to infinity 3/(n+n^1/2)

Problem 2

n=1 to infinity 1+cos n/ n^2 - Mar 22nd 2009, 04:00 PMskeeter
- Mar 22nd 2009, 04:09 PMPlato
$\displaystyle \begin{gathered}

\frac{3}

{{n + \sqrt n }} \geqslant \frac{3}

{{2n }} \hfill \\

\frac{{1 + \cos (n)}}

{{n^2 }} \leqslant \frac{2}

{{n^2 }} \hfill \\

\end{gathered}

$