For the convergent alternating series ${\displaystyle \underset{k=0}{\overset{}{}}}\frac{(-1{)}^k}{(2k+3)!},$ evaluate the $nth$ partial sum for $n=3.$ 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 $ofnis$

$(Roundto$ seven decimal places $as$ needed.$)$