Question

Determine whether the geometric series is convergent or divergent. 10−4+1.6−0.64+…

If it is convergent, find its sum.

Answer 1

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.