Sequence And Series Question 613
Question: The value of $ 0.\overset{\bullet \bullet ,}{\mathop{234}}, $ is
[MNR 1986; UPSEAT 2000]
Options:
A) $ \frac{232}{990} $
B) $ \frac{232}{9990} $
C) $ \frac{232}{990} $
D) $ \frac{232}{9909} $
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Answer:
Correct Answer: A
Solution:
$ 0.\overset{,\bullet \bullet }{\mathop{234}},=0.2343434….. $ = $ \therefore $ = $ 0.2+\frac{34}{1000}+\frac{34}{100000}+\frac{34}{10000000}+…..\infty $ $ =\frac{2}{10}+34[ \frac{1}{10^{3}}+\frac{1}{10^{5}}+\frac{1}{10^{7}}+……..\infty ] $ $ =\frac{2}{10}+34[ \frac{1/10^{3}}{1-1/1000} ]=\frac{2}{10}+34\times \frac{1}{1000}\times \frac{100}{99} $ $ =\frac{2}{10}+\frac{34}{990}=\frac{232}{990} $ .
BETA
