Question

does cos(2/n) converge?

Answer 1

\[\lim_{n\to\infty}\cos(2/n)=\cos(0)=1\]

Answer 2

well, as n goes to infinity, or to zero?

Answer 3

the sequence
\[\frac{2}{n}\]
converges to 0 as n gets larger and larger, so the sequence:
\[\cos(\frac{2}{n}) \rightarrow \cos(0) = 1\]

Answer 4

thank you

Answer 5

i can never remember what the restrictions are for converging or diverging

Answer 6

It diverges based off the nth term test for divergence. Which is what Zarkon wrote. The only way a series can converge is if the lim is zero.
\[\sum_{n=1}^{\infty}a_n\]
converges if and ONLY if
\[\lim_{n \rightarrow \infty}a_n=0\]

Answer 7

i think hes talking about the sequence, not the series.

Answer 8

that is not true

Answer 9

For series, it is true. It is not true for sequences.

Answer 10

Well, that is misleading I suppose. The limit can be zero and it can still diverge. But I mean, if it converges, the lim is zero.

Answer 11

\[\lim_{n\to\infty}a_n=0\] is a necessary condition not a sufficient condition

Answer 12

That's what I meant.

Answer 13

hokiefan, do you got to virginia tech?