Question

Tìm x biết \(\frac{x-1}{2017}\)+\(\frac{x-2}{2016}\)+\(\frac{x-3}{2015}\)+....+\(\frac{x+2017}{1}\)=2017

Answer 1

Hình như đề sai dấu, mình sửa lại rồi!

\(\frac{x-1}{2017}+\frac{x-2}{2016}+\frac{x-3}{2015}+...+\frac{x-2017}{1}=2017\)

\(\Leftrightarrow\) \(\frac{x-1}{2017}-1+\frac{x-2}{2016}-1+\frac{x-3}{2015}-1+...+\frac{x-2017}{1}-1=0\)

\(\Leftrightarrow\) \(\frac{x-2018}{2017}+\frac{x-2018}{2016}+\frac{x-2018}{2015}+...+\frac{x-2018}{1}=0\)

\(\Leftrightarrow\) (x - 2018)\(\left(\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}+...+1\right)=0\)

\(\Leftrightarrow\) x - 2018 = 0

\(\Leftrightarrow\) x = 2018

Vậy S = {2018}

Chúc bn học tốt!!