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The first term of an infinite geometric series is 2 and its sum be denoted by S. If | S – 2 | < 1/10 then the true set of the range of common ratio of the series is
1. \(\left( {\frac{1}{{10}},\;\frac{1}{5}} \right)\)
2. \(\left( { - \frac{1}{2},\;\frac{1}{2}} \right)\) – {0}
3. \(\left( { - \frac{1}{{19}},\;\frac{1}{{20}}} \right)-{\rm{ }}\left\{ 0 \right\}\)
4. \(\left( { - \frac{1}{{19}},\;\frac{1}{{21}}} \right)-{\rm{ }}\left\{ 0 \right\}\)

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Correct Answer - Option 4 : \(\left( { - \frac{1}{{19}},\;\frac{1}{{21}}} \right)-{\rm{ }}\left\{ 0 \right\}\)
\(\left| {\frac{2}{{1 - r}} - 2} \right| < \frac{1}{{10}} \Rightarrow \left| {\frac{1}{{1 - r}} - 1} \right| < \frac{1}{{20}} \Rightarrow \left| {\frac{{1 - 1 + r}}{{1 - r}}} \right| < \frac{1}{{20}} \Rightarrow \left| {\frac{r}{{1 - r}}\,} \right| < \frac{1}{{20}}\)

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