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Math Help - comparison tests

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by TAG16 View Post
    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
    .
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    \begin{gathered}<br />
  \frac{3}<br />
{{n + \sqrt n }} \geqslant \frac{3}<br />
{{2n }} \hfill \\<br />
  \frac{{1 + \cos (n)}}<br />
{{n^2 }} \leqslant \frac{2}<br />
{{n^2 }} \hfill \\ <br />
\end{gathered} <br />
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