The convergence of an infinite seqeunce Suppose that 
$$
a_n = \prod_{k=n}^{\infty}\left(1 - \frac{1}{k^2}\right),
$$ 
for $n \geq 2$. How can we show that 
$$
\lim_{n \to \infty} a_n = \lim_{n \to \infty}\prod_{k=n}^{\infty}\left(1 - \frac{1}{k^2}\right) = 1?
$$ 
Thanks very much.

prove that $\prod_{k=n}^{m}1-\frac{1}{k^2}=\frac{(1+m)(n+1)}{mn}$
