Question

n! +(n+1)!+(n-1)! \(n-2)! ?
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Answer 1

(n!+(n+1)!+(n-1)!)/(n-2)! = (n-2)! ( (n-1)n+n(n-1)(n+1)+(n-1) ) / (n-2)!

Simplificam cu (n-2)! si obtinem:

(n-1)n+n(n-1)(n+1)+(n-1)=(n-1)[n+n(n+1)+1]=(n-1)(n^2+2n+1)= (n-1)(n+1)²