1. ## Inequalities Q

hey, can you guys give me a hand on this question:

Prove $\displaystyle \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}$

thanks

2. Originally Posted by vuze88
hey, can you guys give me a hand on this question:

Prove $\displaystyle \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}$

thanks
$\displaystyle \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}\Leftrightarrow\frac{\ln 1+...+\ln n}{n}<\frac{\ln 1+...+\ln n+1}{n+1}$$\displaystyle \Leftrightarrow \ln 1+...+\ln n<n\ln n+1$.The last inequality is obvious.