Sequence And Series Question 628
Question: The value of $ \overline{0.037} $ where, $ \overline{.037} $ stands for the number 0.037037037…….. is
[MP PET 2004]
Options:
A) $ \frac{37}{1000} $
B) $ \frac{1}{27} $
C) $ \frac{1}{37} $
D) $ \frac{37}{999} $
Show Answer
Answer:
Correct Answer: D
Solution:
Given series 0.037037037?? = 0.037+0.000037+0.0000000037+??. = $ \frac{37}{10^{3}}+\frac{37}{10^{6}}+\frac{37}{10^{9}}+…… $ = $ 37[ \frac{1}{10^{3}}+\frac{1}{10^{6}}+\frac{1}{10^{9}}+…. ] $ = $ 37[ \frac{1/10^{3}}{1-1/10^{3}} ]=37[ \frac{1}{10^{3}}.\frac{10^{3}}{999} ] $ = $ \frac{37}{999} $ .
BETA
