`lim_(n->oo)(1^2+2^2+3^2++n^2)/(n^3)` is equal to a. 1 b . c. 1/3 d. 0

Explanation

To solve the limit \( \lim_{n \to \infty} \frac{1^2 + 2^2 + 3^2 + \ldots + n^2}{n^3} \), we can follow these steps:

### Step 1: Use the formula for the sum of squares
The sum of the squares of the first \( n \) natural numbers is given by the formula:
\[ 1^2 + 2^2 + 3^2 + \ldots + n^2 = \frac{n(n + 1)(2n + 1)}{6} \]

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