The sum

\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+\cdots+\dfrac{2021}{2022!}

can be expressed as a-\dfrac{1}{b!}, where a and b are positive integers. What is a+b ?

**Answer Choices**

A. 2020

B. 2021

C. 2022

D. 2023

E. 2024

The sum

\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+\cdots+\dfrac{2021}{2022!}

can be expressed as a-\dfrac{1}{b!}, where a and b are positive integers. What is a+b ?

**Answer Choices**

A. 2020

B. 2021

C. 2022

D. 2023

E. 2024