Question Number 148453 by mathdanisur last updated on 28/Jul/21
$$\frac{\left({n}\:+\:\mathrm{1}\right)!}{{n}!}\:=\:\mathrm{38}\:\:\Rightarrow\:\:{n}=? \\ $$
Answered by puissant last updated on 28/Jul/21
$$\Rightarrow\frac{\left(\mathrm{n}+\mathrm{1}\right)×\mathrm{n}!}{\mathrm{n}!}=\mathrm{38} \\ $$$$\Rightarrow\mathrm{n}+\mathrm{1}=\mathrm{38} \\ $$$$\Rightarrow\mathrm{n}=\mathrm{37}.. \\ $$
Commented by mathdanisur last updated on 28/Jul/21
$${Thank}\:{you}\:{Ser} \\ $$
Answered by Olaf_Thorendsen last updated on 28/Jul/21
$$\frac{\left({n}+\mathrm{1}\right)!}{{n}!}\:=\:\mathrm{38}\:=\:\frac{\left({n}+\mathrm{1}\right){n}!}{{n}!}\:=\:{n}+\mathrm{1} \\ $$$$\Rightarrow\:{n}\:=\:\mathrm{37} \\ $$
Commented by mathdanisur last updated on 28/Jul/21
$${Thank}\:{you}\:{Ser} \\ $$
Answered by Rasheed.Sindhi last updated on 28/Jul/21
$$\frac{\left({n}\:+\:\mathrm{1}\right)!}{{n}!}\:=\:\mathrm{38}\:\:\Rightarrow\:\:{n}=? \\ $$$$\frac{\left({n}\:+\:\mathrm{1}\right)!}{{n}!\left({n}+\mathrm{1}\right)}\:=\:\frac{\mathrm{38}}{{n}+\mathrm{1}}\: \\ $$$$\frac{\left({n}\:+\:\mathrm{1}\right)!}{\left({n}+\mathrm{1}\right)!}\:=\:\frac{\mathrm{38}}{{n}+\mathrm{1}}\: \\ $$$$\:\:\:\:\:\mathrm{1}=\frac{\mathrm{38}}{{n}+\mathrm{1}} \\ $$$$\:\:\:\:{n}+\mathrm{1}=\mathrm{38} \\ $$$$\:\:\:\:\:\:{n}=\mathrm{38}−\mathrm{1}=\mathrm{37} \\ $$
Commented by mathdanisur last updated on 28/Jul/21
$${Thank}\:{you}\:{Ser} \\ $$