Question

By the principle of mathematical induction, prove that, for n > 1

1² + 3² + 5² + ... + (2n - 1)² = (n(2n - 1)(2n + 1))/3 

Answer 1

Let P(n)

∴ P(1) is true 

Let P(n) be true for n = k

∴ P(k + 1) is true 

Thus P(k) is true ⇒ P(k + 1) is true. 

Hence by principle of mathematical induction, P(k) is true for all n ∈ N.