For which values $ofp$ does ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^7}{(n^8+3{)}^{8p}}for$

infinity. Use $an$ appropriate type $of$ parenthesis $"(",")","["or"]"$ depending $on$ whether the interval $is$ open $or$ closed.$a_n=f(n),$ where $fis$ a positive,

decreasing, and continuous function $of$

$x$ for $x1.$

$If{\displaystyle \underset{1}{\overset{}{}}}f(x)dx$ converges, then

${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ converges.

$If{\displaystyle \underset{1}{\overset{}{}}}f(x)dx$ diverges, then

${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ diverges.

Recall that the infinite $p-$series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^p}$

converges $ifp>1$ and

diverges otherwise.