$1pt1$

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Question $9$

The Test for Divergence for infinite series $($also called the $"$n$-$th term test for divergence of a series"$)$ says that:

$\underset{n}{lim}{a}_{n}0=>{\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ diverges

Notice that this test tells us nothing about ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ if $\underset{n}{lim}{a}_n=0$; in that situation the series might converge or it might diverge.

Consider the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5n^3}{6n^{2}6}$

The Test for Divergence tells Us that this series:

might converge or might diverge

converges

diverges

Question $10$

$1$ pt $5$

$1($i$)$

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Compute the value of the following improper integral, if it converges. $($If it diverges, enter oo if it

$74F$

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