Suppose You Wish to Use the Principle of Mathematical Induction $1 \cdot 1 ! + 2 \cdot 2 ! + 3 \cdot 3 ! + \cdots + n \cdot n ! =$

question 40

Short Answer

Suppose you wish to use the Principle of Mathematical Induction to prove that $1 \cdot 1 ! + 2 \cdot 2 ! + 3 \cdot 3 ! + \cdots + n \cdot n ! =$ $( n + 1 ) ! - 1 \quad \text { for all } n \geq 1 \text {. }$
(a) Write P(1)
(b) Write P(5)
(c) Write P(k)
(d) Write P(k+1)
(e) Use the Principle of Mathematical Induction to prove that P(n) is true for all $n \geq 1$

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