Tìm x biết: ( x-2015)n=xm, m thuộc N
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta thấy \(2015-\left|y-2015\right|=y\)nếu \(y\le0\)
và \(2015-\left|y-2015\right|=2015-y+2015\)nếu \(y>2015\)
Nếu \(y\ge2015\)thì \(y-2015-\left|y-2015\right|=y-y=0\)
\(\Leftrightarrow y=0;1;2;3;4;...;2015\)(vì y là số tự nhiên)
Nếu \(y>2015\)thì:
\(y-2015-\left|y-2015\right|=y-2015-y+2015=y-y=0\)
\(\Leftrightarrow y=2016;2017;.....\)
\(\Rightarrow x=0\)
Từ 2 trường hợp trên , ta có:
\(y=0;1;2;3;4;5;...\)hay \(y\in N\)
\(x=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2015 - (x+1) : 3 = 2000
(x+ 1) : 3 = 2015 - 2000
(x + 1): 3 = 15
x + 1 = 45
x = 45 - 1
x = 44
Đúng cho mình nha
2015 - ( x + 1 ) : 3 = 2000
( x + 1 ) : 3 = 2015 - 2000
( x + 1 ) : 3 = 15
x + 1 = 15 . 3
x + 1 = 45
x = 45 - 1
x = 44
![](https://rs.olm.vn/images/avt/0.png?1311)
2015-(x+1):3=2000
=> (x+1):3=2015-2000
=> (x+1):3=15
=> x+1=15.3
=> x+1=45
=> x = 45-1
=> x = 44
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{15}+\frac{1}{21}+...+\frac{2}{x.\left(x+1\right)}=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{30}+\frac{1}{42}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{x}\right)=\frac{806}{2015}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x}=\frac{806}{2015}:2\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x}=\frac{1}{5}-\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x}=\frac{403}{2015}-\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x}=0\)
\(\Rightarrow x=0\)
Vậy \(x=0\)
Chúc bạn học tốt !!!!
\(\Rightarrow\frac{1}{2}\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{806}{2015}.\frac{1}{2}\)
\(\Rightarrow\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{x\left(x+1\right)}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}=\frac{403}{2015}\)
\(\Rightarrow\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+...+\frac{x+1-x}{x\left(x+1\right)}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{5}-\frac{403}{2015}\)
rồi bạn tự giải nốt nhé
![](https://rs.olm.vn/images/avt/0.png?1311)