JEE Mains · Maths · STD 11 - 8. sequence and series
The least positive integer \(n\) such that \(1 - \frac{2}{3} - \frac{2}{{{3^2}}} - .... - \frac{2}{{{3^{n - 1}}}} < \frac{1}{{100}},\) is
- A \(4\)
- B \(5\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(1 - \frac{2}{3} - \frac{2}{{{3^2}}}...\frac{2}{{{3^{n - 1}}}} < \frac{1}{{100}}\) \( \Rightarrow 1 - \frac{2}{3}\left[ {\frac{1}{3} + \frac{1}{{{3^2}}} + \frac{1}{{{3^3}}} + ....\frac{1}{{{3^{n - 1}}}}} \right] < \frac{1}{{100}}\)…
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