Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } ( - \pi ) ^ { n } ?$
A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C)It is absolutely convergent.
D)It is conditionally convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } ( - \pi ) ^ { n } ?$ 
A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C)It is absolutely convergent.
D)It is conditionally convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } ( - \pi ) ^ { n }$ does not converge because the absolute value of the terms does not approach zero as $n$ approaches infinity. For a series to converge, the terms of the series must approach zero. Since $\pi$ is a constant greater than 1, raising it to any power $n$ will not result in the terms approaching zero, regardless of the sign. Therefore, the series is divergent.

Which of the Following Is True for the Infinite Series ∑n=1∞(−π)n?\sum _ { n = 1 } ^ { \infty } ( - \pi ) ^ { n } ?∑n=1∞​(−π)n?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } ( - \pi ) ^ { n } ?$