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Question Number 55099 by Joel578 last updated on 17/Feb/19
$$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:{n}\:\in\:\mathbb{N}, \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{P}_{{r}} ^{{n}} \:=\:\lfloor{n}!\:{e}\rfloor \\ $$$$\mathrm{where}\:\lfloor{x}\rfloor\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\leqslant\:{x} \\ $$$$\mathrm{and}\:{P}_{{r}} ^{{n}} \:=\:\frac{{n}!}{\left({n}\:−\:{r}\right)!} \\ $$
Answered by tm888 last updated on 18/Feb/19
Commented by Learner last updated on 18/Feb/19
$${please}\:{how}\:{can}\:{i}\:{post}\:{image}\:{as}\:{question}/{answer} \\ $$
Commented by Joel578 last updated on 22/Feb/19
Commented by Joel578 last updated on 22/Feb/19
$${there}\:{is}\:{an}\:{option}\:'{more}'\:{in}\:{top}−{right}\:{corner} \\ $$