Which of the following infinite series has a finite sum? Explain your reasoning. a. 1.5+3+6+12+... b. 2+8+32+128+... c. 4+4.2+4.4+4.6+... d. 20+10+5+2.5+...

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asked Jul 27, 2020 156k views

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Issa Chanzi · Answer 1 · 2020-07-31T12:56:13+0000

Answer:

d. 20+10+5+2.5+...

Explanation:

No geometric series with a common ratio of magnitude greater than 1 will have a finite sum. Nor will any arithmetic series.

Those descriptions exclude answer choices a, b, c. Choice d is a geometric series with a common ratio of 1/2, so will have a finite sum. (It is 40.)

Which of the following infinite series has a finite sum? Explain your reasoning. a. 1.5+3+6+12+... b. 2+8+32+128+... c. 4+4.2+4.4+4.6+... d. 20+10+5+2.5+...

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