alleryStart learning →An infinite geometric series has first term 9 and common ratio 4/3. What can be said about its sum?
AIt converges to 27
BIt converges to 36
CIt has no finite sum
DIt converges to 12
Answer & Solution
Correct answer: C. It has no finite sum
1. An infinite geometric series has a defined sum only when the common ratio lies strictly between -1 and 1.
2. Here the ratio is 4/3, which is greater than 1, so each term is larger than the one before it.
3. The running total grows without bound, so no finite sum exists and the series diverges.
4. Options A, B, and D all apply the convergence formula in a case where it is not allowed.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 SERIES AND THEIR NOTATIONS_
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