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# What is the sum of the following infinite geometric series?

Algebra problem.

0.2 + 0.02 + 0.002....

### 2 Answers

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- PuzzlingLv 71 month ago
Check the link at the bottom and read more about geometric sequences and sums.

The infinite sum formula is:

S = a/(1 - r)

a : first term

r : common ratio, note |r| < 1, for the sum to converge

In your case, you have the first term of 0.2 (a = 1/5)

And the common ratio is 0.1 (r = 1/10)

Plugging in the values:

S = 1/5/(1 - 1/10)

S = 1/5 / (9/10)

S = 1/5 * 10/9

S = 1/1 * 2/9

S = 2/9

P.S. You can also use the decimal values:

S = 0.2/(1 - 0.1)

S = 0.2 / 0.9

S = 2/9

Answer:

A) 2/9

As a double-check, if you calculate 2/9, you get 0.222222... which equals 0.2 + 0.02 + 0.002 + ...

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