For the convergent alternating series ${\displaystyle \underset{k=0}{\overset{}{}}}\frac{(-1{)}^k}{(6k+2{)}^2},$ evaluate the $nth$ partial sum for $n=2.$ Then find $an$ upper bound for the error $|S-S_n|in$ using

the $nth$ partial sum $S_{n}to$ estimate the value $of$ the series $S.$

The $nth$ partial sum for the given value $ofnis$

$(Typean$ integer $or$ a decimal. Round $to$ seven decimal places $as$ needed.$)$