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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 \(=\)

  1. A \(\frac{23}{147}\)
  2. B \(\frac{6}{35}\)
  3. C \(\frac{6}{37}\)
  4. D \(\frac{8}{51}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{8}{51}\)

Step-by-step Solution

Detailed explanation

\( S = \sum_{n=1}^{24} \frac{1}{(2n+1)(2n+3)} = \frac{1}{2} \sum_{n=1}^{24} \left( \frac{1}{2n+1} - \frac{1}{2n+3} \right) \)…