Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 7 \sqrt { n } } ?$
A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 5 } { 7 \sqrt { n } } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 7 \sqrt { n } } ?$ 
A)Its sequence of partial sums is bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 5 } { 7 \sqrt { n } } \neq 0$
D)It is convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 7 \sqrt { n } }$ is a p-series with $p = \frac{1}{2}$, which is less than 1. According to the p-series test, a p-series converges if $p > 1$ and diverges if $p \leq 1$. Therefore, this series diverges.

Which of the Following Is True for the Infinite Series ∑n=1∞57n?\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 7 \sqrt { n } } ?∑n=1∞​7n​5​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { 5 } { 7 \sqrt { n } } ?$