Mathematics, 25.10.2020 07:10 20jacksone

How do you do this question?

Answers

Answer from: marziel24

Convergent

Step-by-step explanation:

aₙ = n² 5ⁿ⁻¹ / (-6)ⁿ

aₙ = (-1)ⁿ n² 5ⁿ⁻¹ / 6ⁿ

aₙ = (-1)ⁿ n² 5ⁿ / (5 (6ⁿ))

aₙ = ⅕ (-1)ⁿ n² (5/6)ⁿ

bₙ = ⅕ n² (5/6)ⁿ

bₙ = ⅕ n² / (6/5)ⁿ

lim(n→∞) bₙ

lim(n→∞) [⅕ n² / (6/5)ⁿ]

Use L'Hopitals' rule:

lim(n→∞) [⅖ n / ((6/5)ⁿ ln(6/5))]

Use L'Hopitals' rule again:

lim(n→∞) [⅖ / ((6/5)ⁿ ln(6/5)²)]

The limit is 0, so the series converges.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

drop out of school or go to quizlet, quizlet is better

step-by-step explanation:

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