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.

{(-0.3)ⁿ}

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. The sequence diverges monotonically.
B. The sequence converges monotonically. It converges to ____.
C. The sequence converges by oscillation. It converges to ____.
D. The sequence diverges by oscillation.

Answer 1

C. The sequence converges by oscillation. It converges to 0.

Explanation:

Here as n increases magnitude of function decreases so it converges.

But at any two consecutive integers function sign changes and it oscillates. Thus it is not monotonic,