Question

so sánh n+1/n+2 và n+2/n+3

Answer 1

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

\(\dfrac{n+2}{n+3}=\dfrac{n+3-1}{n+3}=1-\dfrac{1}{n+3}\)

Ta có: n+2<n+3

=>\(\dfrac{1}{n+2}>\dfrac{1}{n+3}\)

=>\(-\dfrac{1}{n+2}< -\dfrac{1}{n+3}\)

=>\(-\dfrac{1}{n+2}+1< -\dfrac{1}{n+3}+1\)

=>\(\dfrac{n+1}{n+2}< \dfrac{n+2}{n+3}\)