Determine whether the geometric series 192 + 48 + 12 + ... converges or diverges, and identify the sum if it exists. A.) Converges: 768

B.) Diverges

C.) Converges; 64

D.) Converges; 256

D.) Converges; 256

Step-by-step explanation:

x0= 192

x1 = 48 = 192/4

x2 = 12 = 192/(4 x 4)

Therefore, this series can be written as:

Applying limits at infinity:

Since the terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

Thus, the answer is D.) Converges; 256

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step-by-step explanation: