The series ${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n1}(\frac{9}{n^{\frac{1}{2}}})$ converges by the Alternating Series Test. You do not need to prove this.$)$

Suppose we want to approximate the sum of this series so that

Recall that

$|R_N|b_{N1}$ where $b_{N1}$ is the absolute value of the term of index $N1.$

Set $b_{N1}<mn>.</mn><mn>0</mn><mn>0</mn><mn>0</mn><mn>1</mn>$ and solve for N $.$

We get $($enter the exact value here; you do not need to simplify it$)$:

$N>$

Now use a calculator $($if necessary$)$ to get a decimal approximation of this value and remember that N must be an integer and it must be ereater than the number above. The smallest integer that satisifes this inequality is $$