What does the ratio test tell us about the series $\sum_{n=1}^{\infty} \frac{n}{2^{n}}$ ?
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 involves taking the limit of the absolute value of the ratio of consecutive terms. For this series, the limit is 0, which is less than 1, indicating that the series converges according to the ratio test.

What Does the Ratio Test Tell Us About the Series ∑n=1∞n2n\sum_{n=1}^{\infty} \frac{n}{2^{n}}∑n=1∞​2nn​

What Does the Ratio Test Tell Us About the Series $\sum_{n=1}^{\infty} \frac{n}{2^{n}}$