COMEDK · Maths · 5. Sequences and Series
If \(S_{n}=\frac{1}{6 \cdot 11}+\frac{1}{11 \cdot 16}+\frac{1}{16 \cdot 21}+\ldots\) to \(n\) terms, then \(6 S_{n}=\)
- A \(\frac{1}{(5 n+6)}\)
- B \(\frac{(2 n-1)}{5 n+6}\)
- C \(\frac{n}{(5 n+6)}\)
- D \(\frac{5 n-4}{5 n+6}\)
Answer & Solution
Correct Answer
(C) \(\frac{n}{(5 n+6)}\)
Step-by-step Solution
Detailed explanation
We have, \(S_{n}=\frac{1}{6 \cdot 11}+\frac{1}{11 \cdot 16}+\frac{1}{16 \cdot 21}+\ldots+n \text { terms }\) \(\quad=\frac{1}{5}\left(\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\ldots \frac{1}{5 n-1}-\frac{1}{5 n+6}\right)\)…
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