Question

For all n ∈ N, by using principle of mathematical induction, then prove that:

1/3.5 + 1/5.7 + 1/7.9 + ... + 1/((2n + 1)(2n + 3)) = n/(3(2n + 3))

Answer 1

Let given statement is P(n) where n ∈ N i.e.,

Hence, given statement is true for n = 1, 

i.e, P(1) is true.

Let given statement is true for n = m, 

i.e, P(m) is true.

Hence, given statement is also true for n = m + 1,

i.e., P(m + 1) is true.

Hence Proved.