Solution
= Solution
At $n=2$, the product is $1-1/4=3/4$, as required. Suppose the formula holds at $n\ge2$. Appending the next factor gives
$$
\prod_{i=2}^{n+1}\left(1-\frac1{i^2}\right)
=\frac{n+1}{2n}\frac{n(n+2)}{(n+1)^2}
=\frac{n+2}{2(n+1)},
$$
which is exactly the formula at $n+1$. Thus <mathematical induction> gives \b[$(n+1)/(2n)$] for every $n\ge2$. The factorization $1-i^{-2}=(i-1)(i+1)/i^2$ also explains the cancellation in this <telescoping product>.