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=(a_1)/(1-q); \ S=(9)/(1-0.1)=(9)/(0.9)=10.`

answer: 10