If the value of the sum `n^(2) + n - sum_(k = 1)^(n) (2k^(3)+ 8k^(2) + 6k - 1)/(k^(2) + 4k + 3)` as n tends to infinity can be expressed in the form `(p)/(q)` find the least value of (p + q) where p, q `in N`

Explanation

To solve the problem, we need to evaluate the limit of the expression as \( n \) tends to infinity:

\[ n^2 + n - \sum_{k=1}^{n} \frac{2k^3 + 8k^2 + 6k - 1}{k^2 + 4k + 3} \]

### Step 1: Simplifying the Summation

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