Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \pi } { 3 + n ^ { 3 } } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \pi } { 3 + n ^ { 3 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { \pi } { 3 + n ^ { 3 } } ?$ 
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { \pi } { 3 + n ^ { 3 } } \neq 0$
D)It is convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { \pi } { 3 + n ^ { 3 } }$ is convergent because the terms $\frac { \pi } { 3 + n ^ { 3 } }$ approach 0 as $n$ approaches infinity, and the series satisfies the conditions of the comparison test, comparing it to a $p$-series with $p > 1$, which is known to converge.

Which of the Following Is True for the Infinite Series ∑n=1∞π3+n3?\sum _ { n = 1 } ^ { \infty } \frac { \pi } { 3 + n ^ { 3 } } ?∑n=1∞​3+n3π​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { \pi } { 3 + n ^ { 3 } } ?$