Answer:
6/5
Divergent
Step-by-step explanation:
aₙ = (-6)ⁿ / (n 5ⁿ⁺²)
aₙ₊₁ = (-6)ⁿ⁺¹ / ((n+1) 5ⁿ⁺³)
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[(-6)ⁿ⁺¹ / ((n+1) 5ⁿ⁺³)] / [(-6)ⁿ / (n 5ⁿ⁺²)]│
lim(n→∞)│[(-6)ⁿ⁺¹ / ((n+1) 5ⁿ⁺³)] × [(n 5ⁿ⁺²) / (-6)ⁿ]│
lim(n→∞)│[(-6)ⁿ⁺¹ / (-6)ⁿ] × [(n 5ⁿ⁺²) / ((n+1) 5ⁿ⁺³)]│
lim(n→∞)│-6 × n / (5 (n+1))│
lim(n→∞) (6n / (5n + 5))
6/5
The limit is greater than 1, so the series diverges.
