[poper]

$a*\frac{1}{a+1}=\frac{a}{a+1}+a+\frac{1}{a+1}=a+1$
$a*\frac{1}{a+1}*\frac{1}{a+2}*\frac{1}{a+3}*....*\frac{1}{a+n}=a+n$
$1*\frac{1}{2}*\frac{1}{3}*\frac{1}{4}*...*\frac{1}{2549}=2549$