Answers Precalculus Infinite Geometric Series — QuizQuestion 1

1

QuizMultiple Choice

Infinite Geometric Series — Quiz

Question 1 • Precalculus

Which geometric series converges?

Answer

A

1 fifth plus 2 fifths plus 4 fifths plus 8 fifths plus dot dot dot

B

1 fifth plus 2 plus 20 plus 200 plus dot dot dot

C

1 fifth plus 6 fifths plus 36 fifths plus 216 fifths plus dot dot dot

D

1 fifth plus 1 over 20 plus 1 over 80 plus 1 over 320 plus dot dot dot

Explanation

A geometric series converges when the absolute value of its common ratio is less than 1. In choice D, each term is one-fourth of the previous term: (1/20) ÷ (1/5) = 1/4, and the later terms follow the same ratio. Since |1/4| < 1, choice D, the series 1/5 + 1/20 + 1/80 + 1/320 + ···, converges.

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