Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } } ?$ 
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } } \neq 0$
D)It is convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } }$ is convergent because the terms of the series approach zero as $n$ approaches infinity, and the series behaves similarly to a p-series with $p > 1$, which is known to converge.

Which of the Following Is True for the Infinite Series ∑n=1∞6n(2n+1)4?\sum _ { n = 1 } ^ { \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } } ?∑n=1∞​(2n+1)46n​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { 6 n } { ( 2 n + 1 ) ^ { 4 } } ?$