Does the infinite geometric series diverge or converge? Explain.
1/5 + 1/10 + 1/20 + 1/40 ...
(1 point)
It diverges; it has a sum.
It diverges; it does not have a sum.
It converges; it has a sum.
It converges; it does not have a sum.
It converges; it has a sum.
An infinite geometric series converges if the common ratio (r) is between -1 and 1. In this case, the common ratio is 1/2 (each term is half of the previous term). Since 1/2 is between -1 and 1, the series converges. The sum of an infinite geometric series can be calculated using the formula S = a / (1 - r), where a is the first term and r is the common ratio. In this case, the first term is 1/5 and the common ratio is 1/2, so the sum would be 1/5 / (1 - 1/2) = 1/5 / 1/2 = 2/5. Therefore, the infinite geometric series given converges and has a sum of 2/5.