For all `n geq1`, prove that `1^2+2^2+3^2+4^2+dotdotdot+n^2=``(n(n+1)(2n+1))/6`

Explanation

To prove the statement \( P(n): 1^2 + 2^2 + 3^2 + \ldots + n^2 = \frac{n(n+1)(2n+1)}{6} \) for all \( n \geq 1 \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We start by verifying the base case, \( n = 1 \).

**Left-hand side (LHS):**
\[
1^2 = 1
...