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n-1-n-38-n-




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

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