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Lecture

Principle of Strong Induction Examples & Solutions

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Department
Mathematics
Course
MATH 135
Professor
Mike Eden
Semester
Fall

Description
Principle of Strong Induction ExamplesWednesday November 02 20111028 AMA sequence is defined byand Find a formula forthat works for every nonnegative integerand prove by induction that worksTrying a few cases What does it look like Beware the danger of patterns Lets prove this by induction Why will we use strong inductionStrong induction is used because the result of each term uses every term prior to the term Thus they all needs to be trueProofBy strong induction on nBase CaseWe are given that The formulagivesalso Induction HypothesisSuppose that the result is true forfor some integer the last base case That is assume thatforInduction ConclusionConsider What are we required to proveWRITE IT DOWNWe want to prove the formula works for Which meansProofSum of geometric seriesTrue for for allExample 2Prove that MATH 135 Page 1
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