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Jee Main 2025 — Medium JEE math MCQ

For positive integers $n$, if $4a_n = (n^2 + 5n + 6)$ and $S_n = \sum_{k=1}^{n} \left( \frac{1}{ak} \right)$, then the value of $507S_{2025}$ is
  1. A. 540
  2. B. 675
  3. C. 1350
  4. D. 135

Solution

The correct option is **B**. (B. 675)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
For positive integers nn, if 4an=(n2+5n+6)4a_n = (n^2 + 5n + 6) and Sn=∑k=1n(1ak)S_n = \sum_{k=1}^{n} \left( \frac{1}{ak} \right), then the value of 507S2025507S_{2025} is
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep