1. convergence prob

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

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