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.

Question

Mathematics

Ross Williams

20 January, 03:47

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.

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Answers (1)

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Camden Boyd · Answer 1

D. The sequence diverges by oscillation.

Step-by-step 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.