Question

Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges. StartSet 1.00004 Superscript n EndSet Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The sequence converges by oscillation. It converges to nothing. B. The sequence converges monotonically. It converges to nothing. C. The sequence diverges monotonically. D. The sequence diverges by oscillation.

Answer 1

D. The sequence diverges by oscillation.

Explanation:

an = (-1.00000004)n

From root test

L = Lim n->infinity (|an|)(1/n)

==> L = Lim n->infinity (|-1.00000004n|)(1/n)

==> L = Lim n->infinity (|-1.00000004|n)(1/n)

==> L = Lim n->infinity |-1.00000004|

==> L = 1.00000004 > 1

Hence series diverges.