SOLUTION: how do you evaluate an infinite geometric series? ex: 1.1+0.11+0.011+..

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Question 483711: how do you evaluate an infinite geometric series?
ex: 1.1+0.11+0.011+..

Answer by MathLover1(6625) About Me  (Show Source):
You can put this solution on YOUR website!

In a geometric series, finite or infinite, the common ratio is the multiplier used to get each succeeding term. Or, you can think of it as any term divided by the previous one.
For example, in the series you have

1.1+0.11+0.011+.............the common ratio is 0.1
If an infinite geometric series has a ratio whose absolute value is less than 1, and so has a sum, the formula is
S%28inf%29+=+a+%2F+%281-r%29
where S%28inf%29 just stands for the sum of an infinite series,+a is the first term, and r is the common ratio.
in your case:
S%28inf%29+=+1.1+%2F+%281-0.1%29
S%28inf%29+=+1.1+%2F+%280.9%29
S%28inf%29+=+1.2222222222222222222222222222222

S%28inf%29+=+1.2