PIMSO 2022 - Mathematics - Grade 5 - National Round Question 14

Simplify: $2{,}023\left[\frac{1}{2\times1}+\frac{2}{3\times4}+\frac{3}{4\times9}+\frac{4}{5\times16}+\cdots+\frac{2{,}021}{2022\times2{,}021^2}+\frac{2{,}022}{2023\times2{,}022^2}\right]$.