Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 4 } { ( 3 n + 1 ) ^ { n } } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 4 } { ( 3 n + 1 ) ^ { n } } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 4 } { ( 3 n + 1 ) ^ { n } }$ is convergent because the terms of the series approach zero as $n$ approaches infinity, which can be shown using the limit comparison test or the ratio test. The denominator grows much faster than the numerator, ensuring the terms decrease to zero, satisfying the necessary condition for convergence.

Which of the Following Is True for the Infinite Series ∑n=1∞4(3n+1)n?\sum _ { n = 1 } ^ { \infty } \frac { 4 } { ( 3 n + 1 ) ^ { n } } ?∑n=1∞​(3n+1)n4​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { 4 } { ( 3 n + 1 ) ^ { n } } ?$