AP EAMCET · Maths · Sequences and Series
\(\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\frac{1}{7 \cdot 9}+\ldots\) to 24 terms \(=\)
- A \(\frac{23}{147}\)
- B \(\frac{6}{35}\)
- C \(\frac{6}{37}\)
- D \(\frac{8}{51}\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{51}\)
Step-by-step Solution
Detailed explanation
\( S = \sum_{n=1}^{24} \frac{1}{(2n+1)(2n+3)} = \frac{1}{2} \sum_{n=1}^{24} \left( \frac{1}{2n+1} - \frac{1}{2n+3} \right) \)…
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