Let the sequence Tn be defined by T1 = T2 = T3 = 1 and Tn = Tn-1 + Tn-2 + Tn-3 for n ≥ 4. Use induction to prove that Tn < 2n for n ≥ 4
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Let be the proposition that
Basis Step
is true, because
Inductive Step
We assume that
Under this assumption
is true under the assumption that is true. This completes the inductive step.
We have completed the basis step and the inductive step, so by mathematical induction we
know that is true for all That is, we have proved that