# MI - Mathematical Induction We use Mathematical Induction...

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Mathematical Induction We use Mathematical Induction to prove the truth of a statement. It can be used to prove simple mathematical identities like N i =1 i = N ( N +1) 2 to statements like the ”A polygon has many sides as it has angles”. In general the statement is made on some property that applies to natural numbers (for example N in the above example). The steps involved in a proof by Mathematical induction are: Step 1: Basis Show that the statement is true for some base cases, say N=1, 2 etc. Step 2: Inductive Hypothesis Assume that the statement is true for some natural number N = k . Step 3: Inductive Step Using the inductive hypothesis prove that the statement is true for N = k + 1 as well. We will take two examples of Mathematical Induction On Fibonacci Numbers Lets prove the following statement by following the process of Mathematical Induction: The sum of the ﬁrst N odd Fibonacci numbers is equal to the (2N)th Fibonacci number The given statement can be written as: F

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MI - Mathematical Induction We use Mathematical Induction...

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