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[Solved] Factorial

 
Basics of Algebra
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June 14, 2021 5:43 pm
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(@armor)
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\frac{(k+1)!-k!}{(k-1)!+(k-2)!}=56\Rightarrow k=?

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June 14, 2021 5:43 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

\small \frac{(k+1)!-k!}{(k-1)!+(k-2)!}=\frac{k!(k+1-1)}{(k-2)!(k-1+1)}=\frac{k!k}{(k-2)!k}

\small =\frac{k(k-1)(k-2)!}{(k-2)!}=k(k-1)=56\Rightarrow k=8.

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