Sequence And Series Question 534
Question: $ 0.\overset{\bullet ,\bullet ,}{\mathop{423}},= $
[Roorkee 1961; IIT 1973]
Options:
A) $ \frac{419}{990} $
B) $ \frac{419}{999} $
C) $ \frac{417}{990} $
D) $ \frac{417}{999} $
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ 0.,4\overset{,.,.,}{\mathop{23,}},=0.4232323……. $ $ =0.4+0.023+0.00023+0.0000023+……..\infty $ $ =\frac{4}{10}+\frac{23}{10^{3}}+\frac{23}{10^{5}}+\frac{23}{10^{7}}……..\infty $ $ =\frac{4}{10}+\frac{23}{10^{3}}[ 1+\frac{1}{10^{2}}+\frac{1}{10^{4}}+……….\infty ] $ $ =\frac{4}{10}+\frac{23}{1000}( \frac{1}{1-\frac{1}{10^{2}}} )=\frac{4}{10}+\frac{23}{990}=\frac{419}{990} $ .
BETA
