For all `n geq1`, prove that `1^2+2^2+3^2+4^2+.......+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 mathematical induction, we will follow these steps:

### Step 1: Base Case
We start by proving the base case, \( P(1) \).

**Calculation:**
- Left-hand side (LHS):
\[
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