Find the infinity, the sum of the sequence 1, 910 9 10 , (910 9 10 )2, (910 9 10 )3,...

Find the infinity, the sum of the sequence 1, $\frac{9}{10}$, ($\frac{9}{10}$)2, ($\frac{9}{10}$)3,...

Answer Details

To find the sum of the infinite series, we can use the formula for the sum of an infinite geometric series, which is: S = a/(1-r) where a is the first term of the series and r is the common ratio between consecutive terms. In this series, the first term is 1 and the common ratio is (910/9)/(910/10) = 10/9. Therefore, the sum of the series is: S = 1/(1 - 10/9) = 1/(1/9) = 9 Therefore, the correct option is (B) 9.