$(2$ pts$)$ Consider the convergent series:

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{(-1{)}^{k+1}}{(2k+1{)}^2}$

a$.(1$ pt$)$ Estimate the sum of this series by adding the first $3$ terms. $($Write the exact value of the terms you're adding, but you can give a decimal approximation for the final answer $-$ don't mess around with adding fractions.$)$

$S_3=\frac{1}{9}-\frac{1}{25}+\frac{1}{49}$~~$0\mathrm{.}0915193$

b$.(1$ pt$)$ What is the maximum $($absolute$)$ error between what you computed in $($a$),$ and the actual sum of the series? Where does this number come from?

Complete part b and show all work.