x2-x=2016x2017
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](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)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1x2+2x3+3x4+...+2016x2017
=>3A=3x1x2+3x2x3+3x3x4+...+3x2016x2017
=>3A=(3-0)x1x2+(4-1)x2x3+(5-2)x3x4+...+(2018-2015)x2016x2017
=>3A=1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+...+2016x2017x2018-2015x2016x2017
=>3A=2016x2017x2018
=>A=\(\frac{2016\times2017\times2018}{3}\)(tự tính nha)
S = 1x2 + 2x3 + 3x4 + 4x5 + ... + 2016x2017
3S = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 2016x2017x(2018-2015)
3S = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 2016x2017x2018 - 2015x2016x2017
3S = 2016x2017x2018
S = 1/3 x 2016x2017x2018.
![](https://rs.olm.vn/images/avt/0.png?1311)
2016 × 2018 - 1/2015 + 2016 × 2017
= 2016 × (2017 + 1) - 1/2015 + 2016 × 2017
= 2016 × 2017 + (2016 - 1)/2015 + 2016 × 2017
= 2016 × 2017 + 2015/2015 + 2016 × 2017
= 1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2015+2016.2017}{2017.2018-2019}\)
\(=\frac{2015+2016.2017}{2017.\left(2016+2\right)-2019}\)
\(=\frac{2015+2016.2017}{2017.2016+4034-2019}\)
\(=\frac{2015+2016.2017}{2017.2016+2015}\)
\(=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1X2 +2x3 +...+ 2016x2107
3A = 1x2x3 + 2x3x3 + ...+ 2016x2017x3
3A = 1x2x(3-0) + 2x3x(4-1) + ... + 2016x2017x(2018-1)
3A = 1x2x3 - 1x2x0 +2x3x4 -1x2x3 +...+ 2016x2017x2018 - 2016x2017x2015
Ta loại trừ còn
3A = 2016x2017x2018 - 1x2x0
3A = 2016x2017x2018
A = 2016 x2017 x2018 : 3
A = 1x2 +2x3 +3x4 +...+ 2016 x 2017
3A = 1x2x3 + 2x3x3 +...+2016 x 2017 x3
3A = 1x2x(3-0) + 2x3x(4-1) +...+ 2016x2017x(2018-2015)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2015\times2016}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2015}-\frac{1}{2016}\)
\(=1-\frac{1}{2016}=\frac{2015}{2016}\)
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2015\cdot2016}+\frac{1}{2016\cdot2017}\)
\(\frac{2-1}{1\cdot2}+\frac{3-2}{2\cdot3}+\frac{4-3}{3\cdot4}+...+\frac{2016-2015}{2015\cdot2016}+\frac{2017-2016}{2016\cdot2017}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2016}-\frac{1}{2017}\)(làm gọn một chút)
\(1-\frac{1}{2017}=\frac{2016}{2017}\)
x^2 - x = 2016 * 2017
x * ( x - 1 ) = 2017 * ( 2017 - 1 )
Vậy x = 2017
\(x^2-x=2016\cdot2017=4066272\Rightarrow x^2-x+\frac{1}{4}=4066272+\frac{1}{4}=4066272,25\)
\(\Rightarrow x^2-2\cdot\frac{1}{2}x+\left(\frac{1}{2}\right)^2=\left(x-\frac{1}{2}\right)^2=\left(x-0,5\right)^2=4066272,25\Rightarrow x-0,5=+-2016,5\)
\(\Rightarrow x-0,5=2016,5\Rightarrow x=2016,5+0,5=2017\)
\(x-0,5=-2016,5\Rightarrow x=-2016,5+0,5=-2016\)
vậy x=2017 và x=-2016