NL-NWO 1986 Problem 2

Prove that for all positive integers $n$ holds that $$\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+...+\frac{1}{(2n-1) \cdot 2n}=\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}$$