Tính S=(1\9-1)(1/10-1)...(1/2018-1)(1/2019-1)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=1+(2-3)+(-4+5)+(6-7)+(-8+9)+...+(-2020+2021)
S=1-1+1-1+1+...+1
S=1+0+0+...+0
S=1
\(S=1+2-3-4+...+2017+2018-2019-2020+2021\\ S=\left(1+2-3-4\right)+...+\left(2017+2018-2019-2020\right)+2021\\ S=\left(-4\right)+\left(-4\right)+\left(-4\right)+...+-4+2021\\ S=505.\left(-4\right)+2021\\ S=-2020+2021\\ S=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(S=1+2-3-4+5+6-...+2018-2019-2020+2021\)
\(=\left(-4\right)\cdot505+2021\)
=2021-2020
=1
\(S=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(2017+2018-2019-2020\right)+2021\\ S=\left(-4\right)+\left(-4\right)+...+\left(-4\right)+2021\)
Ta có từ 1 đến 2020 có 2020 số nên khi nhóm 4 số 1 cặp thì có \(2020:5=404\left(cặp\right)\)
Vậy \(S=404\left(-4\right)+2021=-1616+2021=405\)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=1+2-3-4+5+6-7-8+9+10-...+2018-2019-2020+2021
=1+(2-3-4+5)+(6-7-8+9)+...+(2018-2019-2020+2021)
=1+0+0+...+0
=1
Vậy S=1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=1+2-3-4+5+6-7-8+9+10-...+2018-2019-2020+2021\)
\(S=0+1-1+1-1+...-1-+1=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = (-1)(-1)^2(-1)^3...(-1)^2019
A = (-1)^1+2+3+...+2019
A = (-1)^2039190
A = 1
S = 1.2.3 + 2.3.4 + 3.4.5 + ... + 2018.2019.2020
4S = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + .... + 2018.2019.2020.4
4S = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 2018.2019.2020.(2021 - 2017)
4S = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 2018.2019.2020.2021 - 2017.2018.2019
4S = 2018.2019.2020.2021
S = 2018.2019.2020.2021 : 4 = ...