Question Number 1729 by Rasheed Ahmad last updated on 04/Sep/15 | ||
$${Prove}/{disprove}/{prove}\:{for}\:{an} \\ $$ $${interval}\:{as}\:{the}\:{case}\:{may}\:{be}: \\ $$ $$\left({x}!\right)^{\frac{\mathrm{1}}{{x}}} \:\overset{?} {<}\:\left\{\left({x}+\mathrm{1}\right)!\right\}^{\frac{\mathrm{1}}{{x}+\mathrm{1}}} \:\:,\:{x}\in\mathbb{N}\:\left[{x}\neq\mathrm{0}\right] \\ $$ $$\left({Generalization}\:{of}\:{Q}\:\mathrm{1700}\right) \\ $$ | ||
Commented by123456 last updated on 04/Sep/15 | ||
$${x}\in\mathbb{N}^{\ast} \left({x}\neq\mathrm{0}\right) \\ $$ | ||
Commented by123456 last updated on 04/Sep/15 | ||
$${f}\left({x}\right)=\left({x}!\right)^{\frac{\mathrm{1}}{{x}}} \\ $$ $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}{f}\left({x}\right)=? \\ $$ | ||
Commented byRasheed Ahmad last updated on 04/Sep/15 | ||
$${Thanks}!\:{Question}\:{is}\:{corrected}. \\ $$ | ||