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