# Math Help - comparison tests

1. ## comparison 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

2. Originally Posted by TAG16
How would you figure out if the series converge or diverge?

Problem 1

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

limit comparison with the divergent series 3/n

Problem 2

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

direct comparison with the convergent series 2/n^2
.

3. $\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}
$