Regarding the series 3 − 3 + 3 − 3 + 3 − …, which is correct?

Correct answer: d i, ii and iii

uₙ = 3(−1)ⁿ⁻¹, u₁₅ = 3 and 15 pairs sum to 0; all three are true.

Why the other options are wrong

• a i and ii: iii is also true: the pairs 3 − 3 give 0, the first 30 terms hold 15 pairs, sum 0; so a true statement is left out.
• b i and iii: ii is also true: 15 is odd, u₁₅ = 3(−1)¹⁴ = 3; so a true statement is left out.
• c ii and iii: i is also true: n = 1, 2, 3 give 3, −3, 3; so a true statement is left out.