A) \[1-{{\left( \frac{1}{10} \right)}^{100}}\]
B) \[1+{{\left( \frac{1}{10} \right)}^{100}}\]
C) \[\]\[1-{{\left( \frac{1}{10} \right)}^{106}}\]
D) \[1+{{\left( \frac{1}{10} \right)}^{100}}\]
Correct Answer: A
Solution :
Series is a G.P. with \[a=0.9=\frac{9}{10}\] and \[r=\frac{1}{10}=0.1\] \[\therefore \]\[{{S}_{100}}=a\left( \frac{1-{{r}^{100}}}{1-r} \right)=\frac{9}{10}\left( \frac{1-\frac{1}{{{10}^{100}}}}{1-\frac{1}{10}} \right)=1-\frac{1}{{{10}^{100}}}\].
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