Question

Giải BĐT:

\(4\le n!+\left(n+1\right)!< 50\)

Answer 1

\(4\le n!+\left(n+1\right)!< 50\\ \Leftrightarrow4\le n!+n!\left(n+1\right)< 50\)

\(\Leftrightarrow4\le n!\left(n+2\right)< 50\)

\(\Rightarrow\left\{{}\begin{matrix}n!\left(n+2\right)\ge4\Rightarrow n\ge2\\n!\left(n+2\right)< 50\left(\cdot\right)\end{matrix}\right.\)

Giải(*) \(n!\left(n+2\right)< 50\)

*)xét n=4

\(\Rightarrow4!\left(4+2\right)=144\left(loại\right)\)

*)xét n=3

\(\Rightarrow3!\left(3+2\right)=30\left(T/m\right)\)

\(\Rightarrow2\le n\le3\Rightarrow n=\left\{2;3\right\}\)