How can I find $\lim_{n\to \infty} a_n$ 
Let $$a_n=\left(1-\dfrac{1}{\sqrt2}\right)\dots \left(1-\dfrac{1}{\sqrt{n+1}}\right),n\ge1$$ Then find $\lim_{n\to \infty} a_n$.

How can I proceed? I am stuck at the first step. Please help.

If you consider $b_n=\ln a_n$, what can you say about the behavior of the sequence $(b_n)_{n\geq 2}$?
