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

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.