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AP EAMCET · Maths · Sequences and Series

\(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+\ldots\) to 50 terms \(=\)

  1. A \(\frac{50}{203}\)
  2. B \(\frac{50}{609}\)
  3. C \(\frac{150}{203}\)
  4. D \(\frac{25}{609}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{50}{609}\)

Step-by-step Solution

Detailed explanation

\(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+\ldots\) \(T_n=\frac{1}{(4 n-1)(4 n+3)}=\frac{1}{4}\left[\frac{1}{4 n-1}-\frac{1}{4 n+3}\right]\) \(T_1=\frac{1}{4}\left[\frac{1}{3}-\frac{1}{7}\right] \Rightarrow T_2=\frac{1}{4}\left[\frac{1}{7}-\frac{1}{11}\right]\)…