Ta có:
A=1/2+ 1/22+ ....+ 1/22019
2A= 2(1/2+ 1/22+...+1/22019 )
2A= 1+1/2+1/22+....+1/22018
2A-A= ( 1+1/2+1/22+....+1/22018) - (1/2+1/22+...+1/22019)
= 1- 1/22019
A= 1-1/22019= 22020/22019 - 1/22019= 22019+ 1/22019
Vậy 1/2+ 1/22+...+ 1/22019 = 22019+1/ 22019