# Thread: convergence prob

1. ## convergence prob

How do I determine if the following converges (using basic convergence tests: comparison, limit comparison, etc.)
$\displaystyle \sum\sin\frac{1}{n}$

2. Originally Posted by manyarrows
How do I determine if the following converges (using basic convergence tests: comparison, limit comparison, etc.)
$\displaystyle \sum\sin\frac{1}{n}$
Compare it to $\displaystyle \sum\frac{1}{n}$. Thus, it diverges.

(See here for a similar problem.)

3. Even on [1,infinity]

It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.

4. Originally Posted by manyarrows
Even on [1,infinity]

It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.
You should read this: http://en.wikipedia.org/wiki/Harmoni...s_(mathematics)

5. Originally Posted by manyarrows
Even on [1,infinity]

It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.
The series in question is not an alternating series.