Determine whether the following sequence converges or diverges...?

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.

thank you! :)

2 Answers

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  • O(n)
    Lv 5
    2 months ago
    Favorite Answer

    C is correct.

    It's a geometric progression with a negative ratio , -0.3, whose absolute value is 0.3 < 1.

    Oscillation is implied by the negative sign of the ratio. This alternates the sign between successive terms.

    Convergence is implied by the absolute value of the ratio being less than 1. All such geometric progressions converge to 0.

    So, the sequence converges by oscillation to 0.

     

  • 2 months ago

    C. The sequence converges by oscillation. It converges to  1/( 1 - (-0.3))

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