The following statement will be proved using mathematical induction.
For the first step, it should be shown that the equation holds true for
The statement is true for
Now, assume that the statement is true for some positive integer
Next, show that the statement is true for
To do so, start by adding
to both sides of the above equation.
Add the terms on the right-hand side, then the of the .
The left-hand side is the sum of the squares of the first
positive integers. The right-hand side is the expression obtained when substituting
Therefore, the statement holds for all positive integers