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
- A \(\frac{3 n}{2(3 n+2)}\)
- B \(\frac{3 n}{3 n+2}\)
- C \(\frac{n}{2(3 n+2)}\)
- D \(\frac{n}{3 n+2}\)
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…
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