11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer \[2.\overset{\bullet \,\,\bullet \,\,\bullet }{\mathop{357}}\,=\] [IIT 1983; RPET 1995]

    A) \[\frac{2355}{1001}\]

    B) \[\frac{2370}{997}\]

    C) \[\frac{2355}{999}\]

    D) None of these

    Correct Answer: C

    Solution :

    Given that \[2.\overset{.\,\,\,.\,\,\,.}{\mathop{357}}\,=2.357357357357......\] \[=2+0.\overset{{}}{\mathop{357}}\,+0.000357+0.000000357+.......\infty \] \[=2+\frac{357}{{{10}^{3}}}+\frac{357}{{{10}^{6}}}+\frac{357}{{{10}^{9}}}+.......\] \[\therefore \] \[{{S}_{\infty }}=2+\frac{\frac{357}{{{10}^{3}}}}{1-\frac{1}{{{10}^{3}}}}=2+\frac{357}{{{10}^{3}}}\times \frac{{{10}^{3}}}{999}=\frac{2355}{999}\].


You need to login to perform this action.
You will be redirected in 3 sec spinner