For which value of the common ratio can the sum to infinity of an infinite geometric series be found?

Correct answer: c −0.5

−1 < −0.5 < 1, that is |r| < 1; so the sum exists.

Why the other options are wrong

• a −2: |−2| = 2 > 1, so the sum cannot be found.
• b −1: For r = −1 the series is a − a + a − …, with no sum.
• d 1.5: 1.5 > 1, so the sum cannot be found; the correct answer is −0.5.