Does the infinite geometric series diverge or converge? Explain.
one over five plus one over ten plus one over twenty plus one over forty+ ...
(1 point)
Responses
It diverges; it has a sum.
It diverges; it has a sum.
It diverges; it does not have a sum.
It diverges; it does not have a sum.
It converges; it has a sum.
It converges; it has a sum.
It converges; it does not have a sum.
It converges; it has a sum.
To determine if the infinite geometric series converges or diverges, we can use the formula for the sum of an infinite geometric series: 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. Plugging these values into the formula, we get:
S = (1/5) / (1 - 1/2)
S = (1/5) / (1/2)
S = (1/5) * (2/1)
S = 2/5
Since the sum of the infinite geometric series is 2/5, it converges to a finite value and thus it converges.