What does the ratio test tell us about the series $\sum_{n=1}^{\infty} \frac{1}{n^{3}}$ ?
A)The series converges.
B)The series diverges.
C)The ratio test doesn't tell us anything about the convergence of the series.

Question

Quizplus · Accepted Answer

The ratio test is inconclusive for this series because the limit of the ratio of consecutive terms is 1, which does not provide information about convergence. However, the series converges by the p-series test with $p = 3 > 1$.

What Does the Ratio Test Tell Us About the Series ∑n=1∞1n3\sum_{n=1}^{\infty} \frac{1}{n^{3}}∑n=1∞​n31​

What Does the Ratio Test Tell Us About the Series $\sum_{n=1}^{\infty} \frac{1}{n^{3}}$