14 **Does the series \(\sum_{n=1}^{\infty} (-1)^n \frac{n^3}{n^5 + 2}\) converge absolutely, converge conditionally, or diverge?**Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.- **A.** The series converges absolutely per the Comparison Test with \(\sum_{n=1}^{\infty} \frac{1}{n^2}\).- **B.** The series converges absolutely because the limit used in the nth-Term Test is \(\boxed{\phantom{0}}\).- **C.** The series converges conditionally per the Alternating Series Test and the Comparison Test with \(\sum_{n=1}^{\infty} \frac{1}{n^2}\).- **D.** The series diverges because the limit used in the nth-Term Test is not zero.- **E.** The series diverges because the limit used in the Ratio Test is not less than or equal to 1.- **F.** The series converges conditionally per the Alternating Series Test and because the limit used in the Root Test is \(\boxed{\phantom{0}}\).

Name: 14 **Does the series \(\sum_{n=1}^{\infty} (-1)^n \frac{n^3}{n^5 + 2}\
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 14 **Does the series \(\sum_{n=1}^{\infty} (-1)^n \frac{n^3}{n^5 + 2}\) converge absolutely, converge conditionally, or diverge?**Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.- **A.** The series co