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AP EAMCET · Maths · Sequences and Series

The sum of first \(n\) terms of \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\ldots\) is

  1. A \(\frac{3 n}{2(3 n+2)}\)
  2. B \(\frac{3 n}{3 n+2}\)
  3. C \(\frac{n}{2(3 n+2)}\)
  4. D \(\frac{n}{3 n+2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{n}{2(3 n+2)}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { (c) Let, } S_n=\frac{1}{2 \cdot 5}+\frac{1}{5 \cdot 8}+\frac{1}{8 \cdot 11}+\ldots . . \text { upto } n \text { terms } \\ & =\frac{1}{3}\left[\frac{1}{2 \cdot 5}+\frac{1}{5 \cdot 8}+\frac{1}{8 \cdot 11}+\ldots . . \text { upto } n \text { terms…