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\(\text{Đầu bài viết khó nhìn thí mồ!! viết lại nhé!!}\)
\(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=\frac{x-1}{2015}+\frac{x-2}{2016}+\frac{x-3}{2017}\)
\(\Rightarrow\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=\frac{x-1}{2015}+1+\frac{x-2}{2016}+1+\frac{x-3}{2017}+1\)
\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}-\frac{x+2014}{2015}-\frac{x+2014}{2016}-\frac{x+2014}{2017}=0\)
\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)
\(\text{Mà }\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\)
\(\text{Nên }x+2014=0\Leftrightarrow x=-2014\)
Đặt \(S=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}{\frac{2017}{1}+\frac{2016}{2}+...+\frac{1}{2017}}\)
Biến đổi mẫu
\(\frac{2017}{1}+\frac{2016}{2}+...+\frac{1}{2017}\)
\(=\left(2017+1\right)+\left(\frac{2016}{2}+1\right)+...+\left(\frac{1}{2017}+1\right)-2017\)
\(=2018+\frac{2018}{2}+...+\frac{2018}{2017}+\frac{2018}{2018}-2018\)
\(=2018.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)\)
\(\Rightarrow S=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}{2018.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)}=\frac{1}{2018}\)
Ta có A= 1/2015 + 2/2016 + 3/2017 + ... +2016/4030- 2016
A= 2015-2014/2015 + 2016-2014/2016 +...+4030-2014/4030-2016
A= 2015/2015-2014/2015+ 2016/2016-2014/2016 + ..... +4030/4030-2014/4030 -2016
A= 1-2014/2015 + 1-2014/2016 +....+1-2014/4030 -2016
A= (1+1+1+1+........+1) -(2014/2015+2014/2016+......+2014/4030) -2016
A=2016 - 2014.(1/2015+1/2016+....+1/4030) -2016
A= (2016 - 2016 ) - 2014. ( 1/2015+1/2016+.....+1/4030)
A=-2014.(1/2015+1/2016+....+1/4030)
mà B = 1/2015+1/2016+....+1/4030
nên A : B = -2014
\(\dfrac{x-1}{2012}+\dfrac{x-2}{2013}+\dfrac{x-3}{2014}=\dfrac{x-4}{2015}+\dfrac{x-5}{2016}+\dfrac{x-6}{2017}\)
\(\Leftrightarrow\left(\dfrac{x-1}{2012}+1\right)+\left(\dfrac{x-2}{2013}+1\right)+\left(\dfrac{x-3}{2014}+1\right)=\left(\dfrac{x-4}{2015}+1\right)+\left(\dfrac{x-5}{2016}+1\right)+\left(\dfrac{x-6}{2017}+1\right)\)
\(\Leftrightarrow\dfrac{x+2011}{2012}+\dfrac{x+2011}{2013}+\dfrac{x+2011}{2014}-\dfrac{x+2011}{2015}-\dfrac{x+2011}{2016}-\dfrac{x+2011}{2017}=0\)
\(\Leftrightarrow\left(x+2011\right)\left(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2015}-\dfrac{1}{2016}-\dfrac{1}{2017}\right)=0\)
\(\Leftrightarrow x=-2011\)( do \(\dfrac{1}{2012}+\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2015}-\dfrac{1}{2016}-\dfrac{1}{2017}\ne0\))
\(\left(\dfrac{2016}{2017}-\dfrac{3}{2015}\right)\div\left(\dfrac{-2}{3}\right)-\left(\dfrac{2012}{2015}-\dfrac{1}{2017}\right)\div\left(\dfrac{-2}{3}\right)\)
\(=\left[\left(\dfrac{2016}{2017}-\dfrac{3}{2015}\right)-\left(\dfrac{2012}{2015}-\dfrac{1}{2017}\right)\right]\div\left(\dfrac{-2}{3}\right)\)
\(=\left(\dfrac{2016}{2017}-\dfrac{3}{2015}-\dfrac{2012}{2015}+\dfrac{1}{2017}\right)\div\left(\dfrac{-2}{3}\right)\)
\(=\left[\left(\dfrac{2016}{2017}+\dfrac{1}{2017}\right)+\left(-\dfrac{3}{2015}-\dfrac{2012}{2015}\right)\right]\div\left(\dfrac{-2}{3}\right)\)
\(=\left[1+\left(-1\right)\right]\div\left(\dfrac{-2}{3}\right)\)
\(=0\div\left(\dfrac{-2}{3}\right)=0\)
mình có gì sai sót xin bạn thông cảm cho
9.5 điểm