Question

s=1x2+2x3+3x4+.........+2020x2021

 

Answer 1

Nguồn: Tính tổng: 1x2 + 2x3 + 3x4 +...+ 2019x2020 + 2020x2021 - Hoc24
Đặt $A=1.2+2.3+3.4+.........+2019.2020+2020.2021$

$\Rightarrow 3A=\mathrm{1.2.3}+\mathrm{2.3.3}+\mathrm{3.4.3}+.....+\mathrm{2019.2020.3}+\mathrm{2020.2021.3}$

$=\mathrm{1.2.3}+\mathrm{2.3.}\left(4-1\right)+\mathrm{3.4.}\left(5-2\right)+.....+\mathrm{2020.2021.}\left(2022-2019\right)$

$=\mathrm{1.2.3}+\mathrm{2.3.4}-\mathrm{1.2.3}+\mathrm{3.4.5}-\mathrm{2.3.4}+...+\mathrm{2020.2021.2022}-\mathrm{2019.2020.2021}$

$=\mathrm{2020.2021.2022}$

$\Rightarrow A=\frac{\mathrm{2020.2021.2022}}{3}$