JEE Mains · Maths · STD 11 - 8. sequence and series
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 :
- A \(540\)
- B \(675\)
- C \(1350\)
- D \(135\)
Answer & Solution
Correct Answer
(B) \(675\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & S_n=\sum_{k=1}^n \frac{4}{K^2+5 k+6} \\ & =\sum_{k=1}^n \frac{4}{(K+2)(K+3)}=4 \sum_{K=1}^n\left(\frac{1}{K+2}-\frac{1}{K+3}\right)\end{aligned}\)…
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