Concept explainers
etimes we cannot use mathematical induction to prove a result we believe to be true, but we can use mathematical induction to prove a stronger result. Because the inductive hypothesis of the stronger result provides more to work with, this process is calledinductive loading.We use inductive loading in Exercise 74-76.76.Suppose that we want to prove that
for all positiveintegers n.
- Show that if we try to prove this inequality using mathematical induction, the basis step works, but the inductive step fails.
for all integersrgreater than 1, which, together with a verification for the case wherer= 1, establishes the weaker inequality we originally tried to prove using mathematical induction.
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