Question

How do you do this question?

Answer 1

1

Inconclusive

Explanation:

aₙ = (-1)ⁿ / (n + 6)

aₙ₊₁ = (-1)ⁿ⁺¹ / (n + 1 + 6)

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 1 + 6)] / [(-1)ⁿ / (n + 6)]│

lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 7)] × [(n + 6) / (-1)ⁿ]│

lim(n→∞)│[(-1)ⁿ⁺¹ / (-1)ⁿ] × [(n + 6) / (n + 7)]│

lim(n→∞)│-1 × [(n + 6) / (n + 7)]│

lim(n→∞) [(n + 6) / (n + 7)]

1

The limit equals 1, so the ratio test is inconclusive.