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**Grillakis** When doing problems that tends to these 3 steps: Basis Step, Inductive Hypothesis and proving the Inductive Step, I am having difficuly understanding the Inductive Hypotheses. How do you know what to assume for the Hypothesis? This is what I have.

Q: Prove that 1 · 1! + 2 · 2! + ··· n · n! = (n + 1)! – 1 whenever n is a positive integer?

I have this:

Basis step:

Let n = 1

n · n! = (n + 1)! – 1

1 · 1! = (1 + 1)! – 1

1 · 1 = (2)! – 1

1 = 1

Since they both equal, the basis step holds.

Inductive Hypothesis:

1 · 1! + 2 · 2! + ··· (k + 1) · (k + 1)! = ((k + 1) + 1)! – 1 Mr F says: No. This is NOT the inductive hypothesis required in Step 2. The inductive hypothesis is 1 · 1! + 2 · 2! + ··· k·k! = (k + 1)! – 1

Would I add a (k + 2)! to both the LHS and RHS?