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 = (-9)ⁿ / (2n+1)!

a_n+1 / a_n = [((-9)ⁿ⁺¹ / (2n+3)!)) ] [(2n+1)! /(-9)ⁿ] = -9 / [(2n+3)(2n+2)]

lim_n→∞ l a_n+1 / a_n l = 0 < 1

By the Ratio Test, the series converges.

Answer 2

You should go back and look at the question I just answered for you.

The answer to this one should be obvious.