This algebraic leap in the induction step confused me.
(k+1)!-1+(k+1)(k+1)!=(1+k+1)(k+1)!-1
Can somebody help me understand the algebra of this?
2026-04-01 15:51:57.1775058717
Confusion with algebraic manipulation of inductive step
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Well, $(k+1)!-1 +(k+1)(k+1)! = (k+1)! + (k+1)(k+1)! - 1 = (1+(k+1))(k+1)! - 1$. In the last equation you just have to pull out $(k+1)!$.