Sequence And Series Question 189
Question: $ 2.\overset{\bullet \bullet \bullet }{\mathop{357}},= $
[IIT 1983; RPET 1995]
Options:
A) $ \frac{2355}{1001} $
B) $ \frac{2370}{997} $
C) $ \frac{2355}{999} $
D) None of these
Show Answer
Answer:
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} $ .
BETA
