Question

xét tính tăng, giảm của các dãy số sau

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

Answer 1

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

\(u_{n+1}=\dfrac{n+3}{n+1}\)

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

\(\Rightarrow u_{n+1}-u_n=\dfrac{n\left(n+3\right)-\left(n+1\right)\left(n+2\right)}{n\left(n+1\right)}\)

\(\Rightarrow u_{n+1}-u_n=\dfrac{n^2+3n-\left(n^2+3n+2\right)}{n\left(n+1\right)}\)

\(\Rightarrow u_{n+1}-u_n=\dfrac{n^2+3n-n^2-3n-2}{n\left(n+1\right)}\)

\(\Rightarrow u_{n+1}-u_n=\dfrac{-2}{n\left(n+1\right)}< 0\)

Vậy dãy số \(u_n\) đã cho là dãy giảm