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.

{(-1.00000005)^n}

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

a. The sequence diverges by oscillation.
b. The sequence converges monotonically. It converges to:________
c. The sequence converges by oscillation. It converges to:________
d. The sequence diverges monotonic ally.

Answer 1

a

Explanation:

(-1.00000005)^n

as n becomes very large, the function increases in both positive and negative direction.

If n=1, -1.00000005

if n=2, 1.0000001

if n= 3, -1.00000015

if n=20, 1.000001

if n=21, -1.00000105