Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 5 ^ { n } } { 7 ^ { n + 1 } } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 5 ^ { n } } { 7 ^ { n + 1 } } \neq 0$
D)It is convergent.
E)It is divergent.

Question

Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { 5 ^ { n } } { 7 ^ { n + 1 } } ?$ 
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C) $\lim _ { n \rightarrow \infty } \frac { 5 ^ { n } } { 7 ^ { n + 1 } } \neq 0$
D)It is convergent.
E)It is divergent.

Quizplus · Accepted Answer

The series is a geometric series with a common ratio of $\frac{5}{7}$, which is less than 1. Therefore, the series converges.

Which of the Following Is True for the Infinite Series ∑n=1∞5n7n+1?\sum _ { n = 1 } ^ { \infty } \frac { 5 ^ { n } } { 7 ^ { n + 1 } } ?∑n=1∞​7n+15n​?

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