Use Power Sums to evaluate
\[
\lim _{N \rightarrow \infty} \sum_{s=1}^{N} \frac{3 s^{2}-2 s-4}{N^{3}}
\]
(Give your answer as a whole or exact number.)
\[
\lim _{N \rightarrow \infty} \sum_{s=1}^{N} \frac{3 s^{2}-2 s-4}{N^{3}}=
\]

Step 1 ：The given expression is a Riemann sum. We can convert it into a definite integral by taking the limit as N approaches infinity. The definite integral will give us the exact value of the sum.

Step 2 ：Let's denote s as s and f as \(3s^{2} - 2s - 4\).

Step 3 ：We are trying to find the integral of f as N approaches infinity.

Step 4 ：However, the integral is not converging, which means the sum is not finite. This is because the function we are integrating is a quadratic function, which grows faster than the linear function in the denominator. Therefore, the sum diverges to infinity.

Step 5 ：\(\boxed{\text{The limit does not exist.}}\)