Ta có:
$\frac{n}{n+1}=1-\frac{1}{n+1}$
$\frac{n+2013}{n+2014}=1-\frac{1}{n+2014}$
Vì n + 1 < n + 2014 => $\frac{1}{n+1}>\frac{1}{n+2014}$
Do đó: $\frac{n}{n+1}<\frac{n+2013}{n+2014}$
vì n<n+1 => n/n+1 < 1 => n/n+1<n+2013/n+1+2013 hay n/n+1<n+2013/n+2014
Đúng thì k mik nha!