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

User Treeden
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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

User Alxnull
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