Use the limit comparison test to determine if the series converges or diverges.
-$$\sum _ { n = 1 } ^ { \infty } \frac { 6 + 1 \sin n } { 5 n ^ { 5 / 4 } + 4 \cos n }$$
A) Diverges
B) Converges

Question

Quizplus · Accepted Answer

Since $ \lim\limits_{n\to \infty} \frac{6+1\sin n}{5n^{5/4}+4\cos n} = \frac{6}{5} > 0 $ and $ \sum\limits_{n=1}^\infty \frac{1}{n^{5/4}} $ is a convergent $ p $-series with $ p = \frac{5}{4} > 1 $, the given series converges by the Limit Comparison Test.

Use the Limit Comparison Test to Determine If the Series ∑n=1∞6+1sin⁡n5n5/4+4cos⁡n\sum _ { n = 1 } ^ { \infty } \frac { 6 + 1 \sin n } { 5 n ^ { 5 / 4 } + 4 \cos n }n=1∑∞​5n5/4+4cosn6+1sinn​

Use the Limit Comparison Test to Determine If the Series $\sum _ { n = 1 } ^ { \infty } \frac { 6 + 1 \sin n } { 5 n ^ { 5 / 4 } + 4 \cos n }$