10
QuizMultiple Choice

Infinite Geometric Series — Quiz

Question 10 • Precalculus

Which geometric series converges?

Answer
A
1 half plus 3 plus 18 plus 108 plus dot dot dot
B
1 half plus 1 fourth plus 1 eighth plus 1 over 16 plus dot dot dot
C
1 half plus 3 halves plus 9 halves plus 27 halves plus dot dot dot
D
1 half plus 1 plus 2 plus 4 plus dot dot dot

Explanation

A geometric series converges when the absolute value of its common ratio is less than 1. In choice B, each term is half the previous term, so the common ratio is 1/2, and the series converges. The other choices have common ratios greater than 1, so their terms do not approach zero.

AI-written and checked against the verified answer.