The problem is, Select the FIRST correct reason on the list why the given series converges.
A. Geometric series
B. Comparison with a convergent p series
C. Integral test
D. Ratio test
E. Alternating series test
I understand all the other sub problems except for this one:
$\sum_1^\infty \frac{\cos(n\pi)}{\ln(6n)}$
The answer is E, Alternating series test. The alternating series test is what you do if an alternating series doesn't converge absolutely using the absolute convergence test right? Anyways, I'm a little stumped on how to solve this problem.
My first thought was to take the absolute value of it, which means $\cos(n\pi)\leq 0$. Therefore the original sum was $\leq \frac{1}{\ln(6n)}$ ... Bla!
Any help would be very much appreciated!