1. Compute:

$$
\frac{1}{2 \sqrt{1}+1 \sqrt{2}}+\frac{1}{3 \sqrt{2}+2 \sqrt{3}}+\frac{1}{4 \sqrt{3}+3 \sqrt{4}}+\cdots+\frac{1}{2019 \sqrt{2018}+2018 \sqrt{2019}}
$$

(7 points)
Answer: $1-\frac{1}{\sqrt{2019}}=\frac{\sqrt{2019}-1}{\sqrt{2019}}$.

Solution: a similar solution to this problem is present in Variant 1 under the same number.