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Know what is meant by proof by Induction Learning Outcomes: PROOF BY INDUCTION Be able to use proof by induction to prove statements

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De Moivre’s Theorem Prove by induction Step 1: Show true for n = 1 Step 2: Assume true for n = k Step 3: Prove true for n = k+1 Step 4: Conclusion

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STEPS PROOF BY INDUCTION Step 1: Show true for n = a (any suitable value) Step 2: Assume true for n = k Step 3: Prove true for n = k+1 Step 4: Conclusion

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Step 1: Show true for n = 1 Step 2: Assume true for n = k Step 3: Prove true for n = k+1 Step 4: Conclusion Example: Prove that is divisible by 3 :divisible be 3 Page 20 Ex 4 1,2,3,4,6a 8,9

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Step 1: Show true for n = 1 Example: Prove that Step 2: Assume true for n = k Step 3: Prove true for n = k+1 ???

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Step 3: Prove true for n = k+1 ???

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Example: Prove that Step 3: Prove true for n = k+1 ??? Step 4: Conclusion x + 1 is a factor Unit 3 Page 141 Ex 3A

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