Sequence And Series Question 556
Question: The sum of 100 terms of the series $ .9+.09+.009……… $ will be
Options:
A) $ 1-{{( \frac{1}{10} )}^{100}} $
B) $ 1+{{( \frac{1}{10} )}^{100}} $
C) $ $ $ 1-{{( \frac{1}{10} )}^{106}} $
D) $ 1+{{( \frac{1}{10} )}^{100}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Series is a G.P. with $ a=0.9=\frac{9}{10} $ and $ r=\frac{1}{10}=0.1 $
$ \therefore $ $ S_{100}=a( \frac{1-r^{100}}{1-r} )=\frac{9}{10}( \frac{1-\frac{1}{10^{100}}}{1-\frac{1}{10}} )=1-\frac{1}{10^{100}} $ .
BETA
