Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \pi ^ { n } } { n ^ { \pi } } ?$
A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \pi ^ { n } } { n ^ { \pi} } = 0$
D)It is convergent.
E)It is divergent.

Question

Quizplus · Accepted Answer

The sequence of partial sums is unbounded and increasing, so the series is divergent.

Which of the Following Is True for the Infinite Series ∑n=1∞πnnπ?\sum _ { n = 1 } ^ { \infty } \frac { \pi ^ { n } } { n ^ { \pi } } ?∑n=1∞​nππn​?

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