Ta có:
M= 1 -1/2 + 1/3 - 1/4 +....+ 1/2017 - 1/2018 + 1/2019
M= (1 + 1/3 +.....+ 1/2017 + 1/2019) - (1/2 + 1/4+....+ 1/2018)
M = (1 + 1/3 + 1/2017 + 1/2019 +1 + 1/2 +...+ 1/1009) - 2(1/2 + 1/4+....+ 1/2018)
M= 1 + 1/2 + 1/3 + 1/4+...+ 1/2018 + 1/2019 - 1 -1/2 -.....- 1/1009
M= 1/1010 + 1/1011 + ....+ 1/2019
=> (M-N)² = ( 1/1010 + 1/1011 + ....+ 1/2019 - 1/1010 - 1/1011 -....-1/2019)
=> (M-N)² = 0² =0
Vậy (M-N)² =0