Prove that `1^2+2^2+dotdotdot+n^2>(n^3)/3,``n in N`

Explanation

To prove that \(1^2 + 2^2 + \ldots + n^2 > \frac{n^3}{3}\) for \(n \in \mathbb{N}\), we will use the formula for the sum of squares and compare it to \(\frac{n^3}{3}\).

### Step-by-step Solution:

1. **Write the formula for the sum of squares**:
The sum of the squares of the first \(n\) natural numbers is given by the formula:
\[
S = 1^2 + 2^2 + \ldots + n^2 = \frac{n(n + 1)(2n + 1)}{6}
...