Question

[POLICE Are Number One]

SO SÁNH ;

\(\frac{n}{n+1}\)+ \(\frac{n+1}{n+2}\)  và   \(\frac{2n+1}{n+3}\) (n thuộc N*)

Answer 1

[Lê Minh Anh]

\(\frac{2n+1}{n+3}=\frac{n+n+1}{n+3}=\frac{n}{n+3}+\frac{n+1}{n+3}\)

Do: \(\frac{n}{n+3}< \frac{n}{n+1};\frac{n+1}{n+3}< \frac{n+1}{n+2}\Rightarrow\frac{n}{n+3}+\frac{n+1}{n+3}< \frac{n}{n+1}+\frac{n+1}{n+2}\Rightarrow\frac{2n+1}{n+3}< \frac{n}{n+1}+\frac{n+1}{n+2}\)