2.357 ^ , , , , =

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MCQ

$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $

A
$\frac{{2355}}{{1001}}$
B
$\frac{{2370}}{{997}}$
✓
$\frac{{2355}}{{999}}$
D
None of these

✓

Answer

Correct option: C.

$\frac{{2355}}{{999}}$

c
(c) Given that $2.\mathop {357}\limits^{.\,\,\,.\,\,\,.} = 2.357357357357......$

$ = 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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