Mark M. answered • 07/20/15
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A series a1+a2+ a3+ a4+ ... is geometric if a2/a1 = a3/a2= a4/a3 = ... = r. r is called the common ratio of the series. If -1<r<1, then the series converges. Otherwise the series diverges.
(a). 10 + 5 + 2.5 + 1.25 + ... is geometric with r = 1/2, so the series converges.
(b). 100 + 90 + 81 + 72.9 + ... is geometric with r = 9/10, so the series converges.
(c). 100 + 50 + 25 + 12.5 + ... is geometric with r = 1/2, so the series converges.
(d). 10 + 15 + 22.5 + 33.75 + ... is geometric with r = 3/2, so the series diverges.
