For positive integers n, if 4a n = (n² + 5n + 6) and S n = Σ k=1 ⁿ (1/a k), then the value of 507 S₂₀₂₅ is:

Sequence and Series: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q87

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSequence and Series179× since 2002

For positive integers

n

, if

4a_n = (n^2 + 5n + 6)

and

S_n = \sum_{k=1}^{n} \left(\frac{1}{a_k}\right)

, then the value of

507 S_{2025}

is:

JEE Main 2025 · January, Unspecified (session-level dataset) · Q87

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSequence and Series179× since 2002

For positive integers

n

, if

4a_n = (n^2 + 5n + 6)

and

S_n = \sum_{k=1}^{n} \left(\frac{1}{a_k}\right)

, then the value of

507 S_{2025}

is: