Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } ?$ 
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } \neq 0$
D)It is convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series is convergent because the terms $\frac { 9 } { n ^ { 2 } + 3 n + 5 }$ approach 0 as $n$ approaches infinity, and the series resembles a p-series with $p > 1$, which is known to converge.

Which of the Following Is True for the Infinite Series ∑n=1∞9n2+3n+5?\sum _ { n = 1 } ^ { \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } ?∑n=1∞​n2+3n+59​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { 9 } { n ^ { 2 } + 3 n + 5 } ?$