Sequence And Series Question 635
Question: The sum of the series $ 6+66+666+………. $ upto $ n $ terms is
[IIT 1974]
Options:
A) $ ({10^{n-1}}-9n+10)/81 $
B) $ 2({10^{n+1}}-9n-10)/27 $
C) $ 2(10^{n}-9n-10)/27 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Given series $ 6+66+666+……..+ $ upto $ n $ terms $ =\frac{6}{9}(9+99+999+….. $ upto $ n $ terms) $ =\frac{2}{3}(10+10^{2}+10^{3}+……….+ $ upto $ n $ terms $ -n $ ) $ =\frac{2}{3}( \frac{10(10^{n}-1)}{10-1}-n )=\frac{1}{27},[20(10^{n}-1)-18n] $ $ =\frac{2({10^{n+1}}-9n-10)}{27} $ .
BETA
