summation - Find the value of the sum $frac{1}{1000*1998}+frac{1}{1001*1997}+cdots+frac{1}{1998*1000}$

Find the value of the sum $\frac{1}{1000*1998}+\frac{1}{1001*1997}+\cdots+\frac{1}{1998*1000}$

I attempted expressing it as a telescoping sum, but I don't know how to.
Also, I was curious, is there a closed formula for the general sum

$\frac{1}{xy}+\frac{1}{(x+1)(y-1)}+\cdots+\frac{1}{yx}$, for positive integers $x