#### Question

Prove the following by using the principle of mathematical induction for all *n* ∈ *N*:

1.3 + 3.5 + 5.7 + ...+(2n -1)(2n + 1) = `(n(4n^2 + 6n -1))/3`

#### Solution

Let the given statement be P(*n*), i.e.,

Thus, P(*k* + 1) is true whenever P(*k*) is true.

Hence, by the principle of mathematical induction, statement P(*n*) is true for all natural numbers i.e., *n*.

Is there an error in this question or solution?

Solution Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1.3 + 3.5 + 5.7 + ...+(2n -1)(2n + 1) = (N(4n^2 + 6n -1))/3 Concept: Principle of Mathematical Induction.