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JEE Math Practice Question

For positive integers $n$, if $4 a_n=\left(n^2+5 n+6\right)$ and $S_n=\sum\limits_{k=1}^n\left(\frac{1}{a_k}\right)$, then the value of $507 S_{2025}$ is :

  1. A.540
  2. B.675
  3. C.1350
  4. D.135

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