Question 29
Let $m,n$ be integers with $1\lt m\le n$. Define
$$f(m,n)=\left(1-\frac1m\right)\left(1-\frac1{m+1}\right)\left(1-\frac1{m+2}\right)\cdots\left(1-\frac1n\right).$$
If $S=f(2,2008)+f(3,2008)+\cdots+f(2008,2008)$, find $2S$.
$$f(m,n)=\left(1-\frac1m\right)\left(1-\frac1{m+1}\right)\left(1-\frac1{m+2}\right)\cdots\left(1-\frac1n\right).$$
If $S=f(2,2008)+f(3,2008)+\cdots+f(2008,2008)$, find $2S$.