Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } ?$ 
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } \neq 0$
D)It is convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 8 } { 3 n ^ { 2 } - 1 }$ is a p-series with $p = 2$ (since the denominator is of the form $3n^2 - 1$, which behaves like $n^2$ for large $n$), and p-series are convergent if $p > 1$.

Which of the Following Is True for the Infinite Series ∑n=1∞83n2−1?\sum _ { n = 1 } ^ { \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } ?∑n=1∞​3n2−18​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { 8 } { 3 n ^ { 2 } - 1 } ?$