I need some help in tackling this problem. Im unsure what test i should use to determine whether this series converges or not. I thinking maybe the comparison test?
(Sum of) n=1, infinity $\displaystyle ncosn / n+5$
I need some help in tackling this problem. Im unsure what test i should use to determine whether this series converges or not. I thinking maybe the comparison test?
(Sum of) n=1, infinity $\displaystyle ncosn / n+5$
($\displaystyle \sum^\infty {n\cos n \over n+5}$ you mean?)
$\displaystyle \Big|{n\cos n \over n+5}\Big| = \Big|{n\over n + 5}\Big||\cos n| = \Big|{n+5-5\over n+5}\Big||\cos n|$ $\displaystyle =\Big|1-{5\over n + 5}\Big||\cos n|$. Does this go to 0 as $\displaystyle n\to\infty$? If not, then the series diverges.
edit: oops, lost the cosine heh