Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + n } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 3 } { n ^ { 2 } + n } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + n }$ is convergent because it is a p-series with $p > 1$ (after simplification, it resembles a series that can be compared to $\sum \frac{1}{n^2}$), and the limit of the terms as $n$ approaches infinity is 0, which is a necessary condition for convergence.

Which of the Following Is True for the Infinite Series ∑n=1∞3n2+n?\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + n } ?∑n=1∞​n2+n3​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { 3 } { n ^ { 2 } + n } ?$