Prove that 1 · 1! + 2 · 2! + · · · + n · n! = (n + 1)! − 1 whenever n is a

Jason Farmer

Jason Farmer

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Prove that 1·1!+2·2!+···+n·n!=(n+1)!1 whenever n is a positive integer.

Answer & Explanation



Skilled2021-11-05Added 92 answers

To proof 11!+22!++nn(n+1)!1 for every positive integer n.
Proof by induction
Let P(n) be 11!+22!++nn11=(n+1)!1
Basis step n=1
We then note P(1) is true.
Induction step let P(k+1) is also true
We need to prove that P(k+1) is also true.
We then note that P(k+1) is also true

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