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 $507 S _ { 2025 }$ is : (1) 540 (2) 675 (3) 1350 (4) 135
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 $507 S _ { 2025 }$ is :\\
(1) 540\\
(2) 675\\
(3) 1350\\
(4) 135