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**laughfactory** We're studying for a test in Calc II, and are stumped on what must be a relatively simple problem:

Determine if the following sequence is convergent or divergent:

$\displaystyle \lbrace n \sin (\frac{1}{n}) \rbrace $

Our best attempts to solve this have been for not.

We've tried the Squeeze Theorem, saying that since we're dealing with all positive terms (as n starts at 0 and goes to infinity) we can squeeze it like so:

$\displaystyle 0 \leq n \sin (\frac{1}{n}) \leq 1 $

But that doesn't squeeze to anything in particular. In this case we know the answer is supposed to be that it converges with $\displaystyle \lim_{n \to \infty} \lbrace a_{n} \rbrace = 1 $.

We can't use L'Hospital's Rule either (if I'm not mistaken).

Any thoughts? How to we prove it's convergent with a lim = 1?