For positive integers \(n\), if \(4 a_n=\left(n^2+5 n+6\right)\) and \(S_n=\sum_{k=1}^n\left(\frac{1}{a_k}\right)\), the…

For positive integers \(n\), if \(4 a_n=\left(n^2+5 n+6\right)\) and \(S_n=\sum_{k=1}^n\left(\frac{1}{a_k}\right)\), then the value of \(507 \mathrm{~S}_{2025}\) is:

[JEE Main 2025, 28 Jan (Shift 2)]