The series

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{(5n+3{)}^2}$

$is$ convergent.

$(A).$ According $to$ the Remainder Estimate for

the Integral Test, the error $in$ the approximation

$s$~~$s_{n}sis$ the value $of$ the infinite sum

and $s_{n}is$ the $n-th$ partial sum$|s-s_n|$

$(B).$ Find the smallest value $ofn$ such that this

upper bound $is$ less than $0\mathrm{.}0001.$

$n=$