Question

Find the sum of the convergent series. 9 + 0.9 + 0.09 + 0.009 + . .

Answer 1

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:

$S=\frac{a_1}{1-q}; \ S=\frac{9}{1-0.1}=\frac{9}{0.9}=10.$

answer: 10