16. The "Prince of Mathematics" Gauss could independently complete the summation of an arithmetic sequence when he was in elementary school, but this time he was stumped by a fractional calculation problem given by his teacher. Can you help him? The problem is:
$$
\frac{1}{2} \times\left(\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\cdots \cdots+\frac{1}{1+2+3+4+\cdots+2019+2020}\right)
$$
$=$ . (Express the result as a simplified fraction)
$\frac{2020}{2021}$