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

Question

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

Quizplus · Accepted Answer

The series converges by the ratio test, as the limit of $ \frac{(n+1)^5}{5^{n+1}} \cdot \frac{5^n}{n^5} $ as $ n $ approaches infinity is less than 1.

Which of the Following Is True for the Infinite Series ∑n=1∞n55n?\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 5 } } { 5 ^ { n } } ?∑n=1∞​5nn5​?

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