MCQ
$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $
- A$\frac{{2355}}{{1001}}$
- B$\frac{{2370}}{{997}}$
- ✓$\frac{{2355}}{{999}}$
- DNone of these
$ = 2 + 0.\mathop {357}\limits^{} + 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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