Prove that: n!(n + 2) = n! + (n + 1)! – InterviewSolution

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1.

Prove that: n!(n + 2) = n! + (n + 1)!

Answer»

Given as

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

Let us consider as RHS = n! + (n + 1)!

n! + (n + 1)! = n! + (n + 1) (n + 1 – 1)!

= n! + (n + 1)n!

= n!(1 + n + 1)

= n!(n + 2)

= L.H.S

L.H.S = R.H.S

Thus, Proved.

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