Tìm x: (1+1/2+1/3+...+1/2013).x+2013=2014/1+2015/2+...+4025/2012+4026/2013
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Ai giúp mình câu này với
(1+1/2+1/3+...+1/2012+1/2013) .x +2013 = 2014+2015/2+...+4025/2012+4026/2013
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
\(\frac{2014}{1}+\frac{2015}{2}+...+\frac{4026}{2013}=1+1+...+1+\left[\left(\frac{2014}{1}-1\right)+\left(\frac{2015}{2}-1\right)+...+\left(\frac{4026}{2013}-1\right)\right]\)
\(=2013+\left(\frac{2013}{1}+\frac{2013}{2}+...+\frac{2013}{2013}\right)=2013+2013\left(1+\frac{1}{2}+...+\frac{1}{2013}\right)\) (1)
Ta kết hợp (1) và đề
=>\(\left(1+\frac{1}{2}+...+\frac{1}{2013}\right)x+2013=2013+2013\left(1+\frac{1}{2}+...+\frac{1}{2013}\right)\)
=> x=2013
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x+2013=\frac{2014}{1}+\frac{2015}{2}+...+\frac{4025}{2012}+\frac{4026}{2013}\)
\(\Leftrightarrow\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=\left(\frac{2014}{1}-1\right)+\left(\frac{2015}{2}-1\right)+...+\left(\frac{4025}{2012}-1\right)+\left(\frac{4026}{2013}-1\right)\)
\(\Leftrightarrow\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=\frac{2013}{1}+\frac{2013}{2}+...+\frac{2013}{2012}+\frac{2013}{2013}\)
\(\Leftrightarrow\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=2013\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)\)
\(\Rightarrow x=\frac{2013\left(1+\frac{1}{2}+\frac{1}{3}+..+\frac{1}{2013}\right)}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}=2013\)
Vậy x = 2013 thoả mãn đề bài.