Question

Does the series of cos (1/n) converge or diverge ? please explain it would be really helpful.

Answer 1

cosine is continuous right?

Answer 2

i assume you mean "sequence" here, not series
unless you are adding

Answer 3

so
\[\lim_{n\to \infty}\cos(\frac{1}{n})=\cos(\lim_{n\to \infty}\frac{1}{n})=\cos(0)=1\]

Answer 4

if it is in fact
\[\sum_{n=1}^{\infty}\cos(\frac{1}{n})\] then that is a totally different story, and i would have to do some thinking

Answer 5

oh, no i wouldn't
the terms do not go to zero, they go to one
so no chance it converges

Answer 6

it is the sum of of cos (1/n)

Answer 7

ok then see answer above
the terms do not even go to zero, they get closer and closer to 1
so the sum cannot converge

Answer 8

clear or no?

Answer 9

Yea I understand. Thanks so much

Answer 10

yw

Answer 11

i have no idea?.? sorrry