Question

Với n là số tự nhiên , so sánh: \(\frac{n}{n+1}và\frac{n+1}{n+2}\)

Answer 1

\(\text{Ta có}:1-\frac{n}{n+1}=\frac{1}{n+1}\) 

\(\text{Ta có}:1-\frac{n+1}{n+2}=\frac{1}{n+2}\)

\(\text{Mà }\frac{1}{n+1}>\frac{1}{n+2}\)

\(\text{Nên }\frac{n}{n+1}>n+\frac{n+1}{n+2}\)

Answer 2

Ta có:

\(\frac{n}{n+1}

Answer 3

\(\text{Ta có : }\frac{n}{n+1}=\frac{n+1}{n+1}-\frac{1}{n+1}=1-\frac{1}{n+1}\)

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

\(\text{Vì }n\in z\text{ nên : }\frac{1}{n+1}1-\frac{1}{n+2}\)

\(\text{Hay }\frac{n}{n+1}>\frac{n+1}{n+2}\)