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8. Sequences and Series
medium
$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $
A
$\frac{{2355}}{{1001}}$
B
$\frac{{2370}}{{997}}$
C
$\frac{{2355}}{{999}}$
D
એકપણ નહીં.
(IIT-1983)
Solution
(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 $ ${S_\infty } = 2 + \frac{{\frac{{357}}{{{{10}^3}}}}}{{1 – \frac{1}{{{{10}^3}}}}} = 2 + \frac{{357}}{{{{10}^3}}} \times \frac{{{{10}^3}}}{{999}} = \frac{{2355}}{{999}}$.
Standard 11
Mathematics