The integral in this exercise converges. Evaluate the integral without using a table.

${\displaystyle \underset{0}{\overset{3}{}}}\frac{27}{\sqrt[\phantom{2}]{{}^{2}7}}d$

${\displaystyle \underset{0}{\overset{3}{}}}\frac{27}{\sqrt[\phantom{2}]{{}^{2}7}}d=$

$($Type an exact answer, using radicals as needed.$)$

Determine if the series converges or diverges. Use any method, and give a reason for your answer.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{8n7}{n(n1)(n2)}$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The series diverges because the limit used in the nth$-$Term Test is $($Type an exact answer.$)$

B$.$ Because $\frac{8n7}{n^{3}3n^{2}2n}\frac{8}{n^2}$ and ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{8}{n^2}$ converges, the series converges by the Direct Comparison Test.

C$.$ Because $\frac{8n7}{n^{3}3n^{2}2n}\frac{8}{n^2}$ and ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{8}{n^2}$ diverges, the series diverges by the Direct Comparison Test.