A) \[\frac{2355}{1001}\]
B) \[\frac{2370}{997}\]
C) \[\frac{2355}{999}\]
D) None of these
Correct Answer: C
Solution :
Given that \[2.\overset{.\,\,\,.\,\,\,.}{\mathop{357}}\,=2.357357357357......\] \[=2+0.\overset{{}}{\mathop{357}}\,+0.000357+0.000000357+.......\infty \] \[=2+\frac{357}{{{10}^{3}}}+\frac{357}{{{10}^{6}}}+\frac{357}{{{10}^{9}}}+.......\] \[\therefore \] \[{{S}_{\infty }}=2+\frac{\frac{357}{{{10}^{3}}}}{1-\frac{1}{{{10}^{3}}}}=2+\frac{357}{{{10}^{3}}}\times \frac{{{10}^{3}}}{999}=\frac{2355}{999}\].
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