Question

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

(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ... + (1/n.(n + 1).(n + 2)) = n(n + 3)/4(n + 1)(n + 2)

Answer 1

Let P(n) 

[Using (i)]

∴ P(k + 1) is true 

Thus p(k) is true ⇒ P(k + 1) is true 

Hence by principle of mathematical induction, p(n) is true for all n ∈ z