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(Solved): Determine whether the following series converges. Justify your answer. \sum_(k=1)^(\infty ) (12k^(2) ...



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.

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