Prove that

$\displaystyle {\prod}_{i=2}^n \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n} $ for integers $\displaystyle n\ge2 $

I want to know - what does the $\displaystyle \prod $ mean? Can I do this question through induction? And how does the $\displaystyle i = 2 $ affect my working - as opposed to $\displaystyle i=0 $ or $\displaystyle i=1 $?

I did attempt this, but I haven't got anywhere near close enough. I, sort of, treated the $\displaystyle \prod $ sign as a $\displaystyle \sum $ - so the term to add on to both sides was $\displaystyle \left(1 - \frac{1}{(k+1)^2}\right) $. So no doubt I was completely wrong there.

Help would be much appreciated. Thanks.