Some statements are false for the first few positive integers, but true for some positive integer m
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Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that Sm is true and that Sk implies Sk+1 when k ≥ m. Use this extended principle of mathematical induction to prove that each statement in Exercises 41–42 is true.
Prove that 2n > n2 for n ≥ 5. Show that the formula is true for n = 5 and then use step 2 of mathematical induction.
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S 2 n for n 5 525 52 32 25 Sk 2k k for k 5 Sk1 2k1k1 ...View the full answer
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