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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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 .
$\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} $
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