What is the sum of the series up to infinity?

Correct answer: b −2/3

a = −1, r = −1/2; S∞ = −1/(1 + 1/2) = −2/3.

Why the other options are wrong

• a −3/2: −3/2 is the reciprocal of the right value; S∞ = a/(1 − r) = −1/(3/2).
• c 2/3: The first term is negative (−1), so the sum is negative; the sign of 2/3 is wrong.
• d 3/2: Both the value and the sign of 3/2 are wrong; the right value is −2/3.