Question

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+...

Answer 1

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.)