A) 40/9
B) 38/81
C) 36/171
D) none of these
Correct Answer: B
Solution :
[b] \[S=\frac{4}{19}+\frac{44}{{{19}^{2}}}+\frac{444}{{{19}^{3}}}+...\] ...(1) \[\Rightarrow \frac{1}{19}S=\frac{4}{{{19}^{2}}}+\frac{44}{{{19}^{3}}}+...\] ...(2) Subtracting (2) from (1), we get \[\frac{18}{19}S=\frac{4}{19}+\frac{40}{{{19}^{2}}}+\frac{400}{{{19}^{3}}}+...\] \[=\frac{\frac{4}{19}}{1-\frac{10}{19}}=\frac{4}{9}\] \[\Rightarrow S=\frac{38}{81}\]
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