What is the sum of the following infinite geometric series?

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 + ...

0.2 + 0.02 + 0.002 + .... = 2/9