Problem #WSP-000377

Problem

Given a series of statements enumerated by the natural numbers, the strong induction principle says the following. Suppose that

• The 1st statement is true (the base case).

• Whenever all statements up to and including the $n$th statement is true, the $(n+1)$th statement is also true (induction step).

Then the statement is true for all natural numbers. Show that the strong induction principle works.