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
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 \[-n\]) \[=\frac{2}{3}\left( \frac{10({{10}^{n}}-1)}{10-1}-n \right)=\frac{1}{27}\,[20({{10}^{n}}-1)-18n]\] \[=\frac{2({{10}^{n+1}}-9n-10)}{27}\].
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