Determine whether the following series converges. Justify your answer.
\sum_(k=1)^(\infty ) (12k^(2)+k)/(8k^(2)-2)
Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) A. The series is a
p
-series with
p=
◻
so the series converges by the properties of a p-series. B. The Ratio Test yields
r=
◻
so the series converges by the Ratio Test. C. The series is a geometric series with common ratio
◻
, so the series diverges by the properties of a geometric series. D. The limit of the terms of the series is
◻
, so the series diverges by the Divergence Test. E. The series is a
p
-series with
p=
◻
so the series diverges by the properties of a p-series. F. The Root Test yields
\rho =
◻
, so the series converges by the Root Test.