MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series
Problem
The series 4−4.8+5.76−6.912+… does not have a finite sum. Which statement best explains why?
(a) r is negative, so the alternating signs prevent the series from approaching any single value.
(b) Because r=−1.2 is less than 1, the terms should approach 0, but the alternating signs make the sum impossible.
(c) The common ratio has absolute value greater than one, so rn does not approach 0 as n increases.
(d) The formula for the sum of an infinite geometric series is valid only when r>0; here r is negative.