For each integer n ? 3, let P(n) be the equation
(a) Is P(3) true? Justify your answer.
(b) In the inductive step of a proof that P(n) is true for all integers n ? 3, we suppose P(k) is true (this is the inductive hypothesis), and then we show that P(k + 1) is true. Fill in the blanks below to write what we suppose and what we must show for this particular equation.
Proof that for all integers k ? 3, if P(k) is true then P(k + 1) is true:
Let k be any integer that is greater than or equal to 3, and suppose that __________.
We must show that __________.
(c) Finish the proof started in (b) above.
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