I'm trying to do a proof by induction question and I'm at the very last part. Apparently $(k+1)!(k+2)-1 = (k+2)!-1$. I have checked using an online calculator.
I don't understand why though.
2026-04-07 03:56:23.1775534183
How does $(k+1)!(k+2)-1 = (k+2)!-1$?
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The recurrence for $n!$ is $n! = n (n-1)!.$ Apply for $n=k+2.$