Question

Using the Mathematical induction, show that for any natural number n ≥ 2,

(1 - 1/2²)(1 - 1/3²)(1 - 1/4²) ... (1 - 1/n²) = (n + 1)/2n

Answer 1

Let P(n) is the statement 

⇒ P(k + 1) is true when P(k) is true so by the principle of mathematical induction P(n) is true.