Lesson 7 de moivre theorem proof by induction
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This document outlines the proof by induction of DeMoivre's Theorem. It presents the three steps of an inductive proof: 1) Show the statement is true for the initial value, here n=1; 2) Assume the statement is true for an arbitrary value k; 3) Show that if true for k then it must also be true for k+1, completing the induction proof that the statement is true for all positive integers n.
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Lesson 7 de moivre theorem proof by induction
- 1. Proof by Induction DeMoivre’s Theorem Typically phrased question: Prove by induction: Where n is any integer Step 1: Consider initial value, mostly n=1 …………………………………………………………………………… So the result is true for n=1. Step 2: Assume the statement is true when n=k, that is if …………………………………………………………………………… Step 3 Now consider n=k+1…………………………………………………. Here prove right hand side equals left hand or vice versa So the statement is true when n=k+1. Therefore since it is true for n=1, by induction it is true for all positive integer values of n.