Example

Indicate which test should be used to determine whether the series below converges or diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{\sqrt[\phantom{2}]{n^{3}5}}{7n^{3}6n^{2}2}$

Solution

Since $a_n$ is an algebraic function of $n,$ we compare the given series with a $p-$series. The comparison series for the $$ is $I{b}_n,$ where $b_n=\frac{\sqrt[\phantom{2}]{n^3}}{7n^3}=\frac{n^{\frac{3}{2}}}{7n^3}=$

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