Question

Determine whether the geometric series 19.2 + 9.6 + 4.8 + ... converges or diverges, and identify the sum if it exists.​

Answer 1

Answer: The infinite geometric series converges to 38.4

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Explanation:

Divide each term by its previous term

term2/term1 = 9.6/19.2 = 0.5

term3/term2 = 4.8/9.6 = 0.5

The common ratio is r = 0.5

Since -1 < r < 1 is true, this means the infinite geometric series converges.

It converges to...

S = a/(1-r)

S = 19.2/(1-0.5)

S = 38.4