## The sum of the squares of the first n odd natural numbers

Posted January 10th, 2008 by Structure

What is the sum of the squares of the first n odd natural numbers?

The answer is:

**Proof 1**:

We will use what we know from this:

The sum of the squares of the first n natural numbers

Let

We have

We want to find

**Proof 2 - Induction proof**

1) For n = 1 it's true.

2) Let's consider that is true for n, and let's prove it for n+1.