TS EAMCET · Maths · Sequences and Series
If \(\frac{1}{2.7}+\frac{1}{7.12}+\frac{1}{12.17}+\frac{1}{17.22}+\ldots\) to 10 terms \(=\mathrm{k}\), then \(\mathrm{k}=\)
- A \(\frac{2}{51}\)
- B \(\frac{5}{51}\)
- C \(\frac{5}{52}\)
- D \(\frac{1}{26}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{52}\)
Step-by-step Solution
Detailed explanation
\(k = \frac{1}{5} \left( \left( \frac{1}{2} - \frac{1}{7} \right) + \left( \frac{1}{7} - \frac{1}{12} \right) + \ldots + \left( \frac{1}{5(10)-3} - \frac{1}{5(10)+2} \right) \right)\) \(k = \frac{1}{5} \left( \frac{1}{2} - \frac{1}{52} \right)\)…
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