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Answer:
2/5
Explanation:
The common ratio is r = (1/10)/(1/5) = 5/10 = 1/2. The first term is a1 = 1/5.
The sum of an infinite geometric series is given by ...
S = a1/(1 -r)
S = (1/5)/(1 -1/2) = (2/10)/(5/10) = 2/5
The sum of the series is 2/5.
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It might stick in your head that the sum of 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... is 2. The given series is 1/5 times that.