Đáp án:
Giải thích các bước giải:
S=1^2+2^2+3^2+.....+2019^2
S=(1.2-1)+(2.3-2)+(3.4-3)+......+(2019.2020-2019)
S=(1.2+2.3+3.4+......+2019.2020)-(1+2+3+.......+2019)
Đặt A =1.2+2.3+3.4+....+2019.2020
3A=1.2.3+2.3.3+3.3.3+.......+2019.2020.3
3A=(1.2.3-0.1.2)+(2.3.4-1.2.3)+(3.4.5-2.3.4)+.........+(2019.2020.2021-2018.2019.2020)
3A=2019.2020.2021
A=673.2020.2021
Đặt B =1+2+3+..+2019
B=100.2019
S673.2020.2021-1010.2019
S=1010(673.2021.2-2019)