Try this solution:
1. Note, that 9*0.1=0.9; 0.9*0.1=0.09; 0.09*0.1=0.009, etc.
It means, the gives series is geometric sequence, where a₁=9, q=0.1.
2. Using a₁=9 and q=0,1 it is possible to calculate the sum of this sequence:
[tex] S=\frac{a_1}{1-q}; \ S=\frac{9}{1-0.1}=\frac{9}{0.9}=10. [/tex]
answer: 10
