Final answer:
The geometric series 10−4+1.6−0.64+... is convergent with a sum of 7.14.
Step-by-step explanation:
To determine whether the geometric series 10−4+1.6−0.64+... is convergent or divergent, 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 10 and the common ratio is -0.4. Plugging these values into the formula, we get:
S = 10 / (1 - (-0.4)) = 10 / 1.4 = 7.14
Therefore, the geometric series is convergent and its sum is 7.14.