Use the Ratio Test to determine whether the series is convergent or divergent. Show all steps.

Question

Use the Ratio Test to determine whether the series is convergent or divergent. Show all steps.

Answer 1

a_n = n! / 94ⁿ

a_n+1 / a_n = [(n+1)! / 94ⁿ⁺¹] [94ⁿ / n!] = (1/94)(n+1)

lim_n→∞ l a_n+1 / a_n l = (1/94)lim_n→∞ (n+1) = ∞

By the Ratio Test, the series diverges.

Answer 2

(n+1)!*94ⁿ/(n!*94ⁿ⁺¹)

You should be able to finish it from here to conclude that the series diverges.

You should really be able to see this without the ratio test:

There are n terms in the numerator and n in the denominator.

For n≥94, each additional factor is greater than 1.

Therefore, the series cannot converge.