Determine whether the following series converges or diverges.
$\sum_{n = 1}^{\infty} \frac{\cos (n π)}{n^{4 / 7}}$
Input $C$ for convergence and $D$ for divergence:

Answer

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Answer

Final Answer: The series $\sum_{n = 1}^{\infty} \frac{\cos (n π)}{n^{4 / 7}}$ converges. Therefore, the answer is $C$ .

Steps

Step 1 ：Determine whether the following series converges or diverges: $\sum_{n = 1}^{\infty} \frac{\cos (n π)}{n^{4 / 7}}$

Step 2 ：The series is an alternating series, since $\cos (n π)$ alternates between 1 and -1 for integer values of n.

Step 3 ：The terms $\frac{1}{n^{4 / 7}}$ are positive, decreasing, and approach 0 as n approaches infinity.

Step 4 ：Therefore, by the Alternating Series Test, the series converges.

Step 5 ：Final Answer: The series $\sum_{n = 1}^{\infty} \frac{\cos (n π)}{n^{4 / 7}}$ converges. Therefore, the answer is $C$ .