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ZILLDIFFEQMODAP$126\mathrm{.}1\mathrm{.}001.$EP$.$

Consider the following power series.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^n}{n}{x}^n$

Let $a_n=\frac{(-1{)}^n}{n}{x}^n.$ Find the following limit$.$

$\underset{n}{lim}|\frac{a_{n+1}}{a_n}|=$

$$

Check which variable$($s$)$ should be in your answer.

Find the interval I and radius of convergence $R$ for the given power series. $($Enter your answer for interval of convergence using interval notation.$)$

$I=$

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$R=$

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