Question

So sánh A=n/n+1+n+1/n+2 B=2n+1/2n+3

Answer 1

Ta có : \(A=\dfrac{n}{n}+1+\dfrac{n+1}{n+2}\left(n\ne0,n\ne-2\right)\)

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

\(=\dfrac{2\left(n+2\right)+n+1}{n+2}\)

\(=\dfrac{2n+4+n+1}{n+2}=\dfrac{3n+5}{n+2}\)

Và \(B=\dfrac{2n+1}{2n+3}\)

Đặt \(n=4\) ta được :

\(A=\dfrac{3.4+5}{4+2}=\dfrac{17}{6}\)

\(B=\dfrac{2.4+1}{2.4+3}=\dfrac{9}{11}\)

Vì \(\dfrac{17}{6}>\dfrac{9}{11}\) nên \(A>B\)