AMC 10B 2022 Problem 9

Past Contests AMC 10 AMC 10B - 2022
, , ,
1

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