Using mathematical induction prove that sum of first N odd integers is | Discrete Structure 2082

Discrete Structure20825 marksMathematical induction

Using mathematical induction prove that sum of first N odd integers is N2N^2N2. [5]

$1 + 3 + 5 + \cdots + (2N-1) = N^2$ --- When N = 1, the first odd integer is 1. - LHS = 1 - RHS = 1² = 1 Since LHS = RHS, the statement holds for N = 1. ✓ --- Assume the statement is true for N = k, i.e., assume: $1 + 3 + 5 + \cdots + (2k-1) = k^2$ --- We must prove the statement is true for ...

$$1 + 3 + 5 + \cdots + (2N-1) = N^2$$ --- When N = 1, the first odd integer is 1. - LHS = 1 - RHS = 1² = 1 Since LHS = RHS, the statement holds for N = 1. ✓ --- Assume the statement is true for N = k, i.e., assume: $$1 + 3 + 5 + \cdots + (2k-1) = k^2$$ --- We must prove the statement is true for ...

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