Use mathematical induction to prove that the sum of the first n odd po | Discrete Structure 2079

Discrete Structure20795 marksMathematical induction

Use mathematical induction to prove that the sum of the first n odd positive integers is n2n^2n2. [5]

Claim: The sum of the first n odd positive integers is n². The first n odd positive integers are: 1, 3, 5, 7, ..., (2n - 1). So we want to prove: $1 + 3 + 5 + \cdots + (2n-1) = n^2$ --- Left-hand side (LHS): The first odd positive integer is 1. Right-hand side (RHS): $n^2 = 1^2 = 1$ . Since LHS ...

Claim: The sum of the first n odd positive integers is n². The first n odd positive integers are: 1, 3, 5, 7, ..., (2n - 1). So we want to prove: $$1 + 3 + 5 + \cdots + (2n-1) = n^2$$ --- Left-hand side (LHS): The first odd positive integer is 1. Right-hand side (RHS): $n^2 = 1^2 = 1$. Since LHS ...

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