1/n+1+1/2014=1+1/2013+1/(n+1)
1/n-1/(N+1)=1/2013-1/2014
1/n*(n+1)=1/(2013*2014)
Do do n=2013
Nho k cho mink nha
\(=>\frac{1}{n}-\frac{1}{n+1}\) \(=\frac{2014}{2013}-\frac{2015}{2014}\)
\(=>\frac{1}{n.\left(n+1\right)}\) \(=\frac{1}{4054182}\)
\(=>n.\left(n+1\right)\) \(=4054182\)
\(=>n=2013\)
Tk mk nhé
\(\frac{1}{n}+\frac{2015}{2014}=\frac{2014}{2013}+\frac{1}{n+1}\)
\(\Rightarrow\frac{1}{n}+1+\frac{1}{2014}=1+\frac{1}{2013}+\frac{1}{n+1}\)
\(\Rightarrow\frac{n+1}{n}+\frac{1}{2014}=\frac{1}{2013}+\frac{n+2}{n+1}\)
Vậy................
Tìm số tự nhiên n thỏa mãn \(\frac{1}{n}+\frac{2015}{2014}=\frac{2014}{2013}+\frac{1}{n+1}\) (*)
Ta có: \(\frac{1}{n}+\frac{2015}{2014}=\frac{2014}{2013}+\frac{1}{n+1}\) \(\Leftrightarrow\frac{1}{n}-\frac{1}{n+1}=\frac{2014}{2013}-\frac{2015}{2014}\) \(\Leftrightarrow\frac{1}{n\left(n+1\right)}=\frac{2014^2-2013.2015}{2013.2014}\) \(\Leftrightarrow\frac{1}{n\left(n+1\right)}=\frac{2014^2-\left(2014-1\right)\left(2014+1\right)}{2013.2014}\Leftrightarrow\)
\(\Leftrightarrow\frac{1}{n\left(n+1\right)}=\frac{1}{2013.2014}\Leftrightarrow n\left(n+1\right)=2013.2014\) Vậy n = 2013
