What does the ratio test tell us about the series $\sum_{n=1}^{\infty} \frac{(-0.125)^{n-1}}{\sqrt{n}}$ ?
A)The series diverges.
B)The series converges.
C)The ratio test doesn't tell us anything about the convergence of the series.

Question

Quizplus · Accepted Answer

The ratio test involves taking the limit of the absolute value of the ratio of consecutive terms. If this limit is less than 1, the series converges. For the given series, the limit of the absolute value of the ratio of consecutive terms is less than 1, indicating convergence.

What Does the Ratio Test Tell Us About the Series ∑n=1∞(−0.125)n−1n\sum_{n=1}^{\infty} \frac{(-0.125)^{n-1}}{\sqrt{n}}∑n=1∞​n​(−0.125)n−1​

What Does the Ratio Test Tell Us About the Series $\sum_{n=1}^{\infty} \frac{(-0.125)^{n-1}}{\sqrt{n}}$