Question

Determine whether the series [infinity] n - 1 2n - 1 n = 1 is convergent or divergent.

1) Convergent
2) Divergent

Answer 1

To determine whether the series [infinity] n - 1 2n - 1 n = 1 is convergent or divergent, we can use the limit comparison test. By comparing this series with the harmonic series, which is a well-known divergent series, we can determine its convergence or divergence.

Step-by-step explanation:

To determine whether the series [infinity] n - 1 2n - 1 n = 1 is convergent or divergent, we can use the limit comparison test. By comparing this series with the harmonic series, which is a well-known divergent series, we can determine its convergence or divergence.

First, let's evaluate the limit of the ratio of the terms of the given series to the terms of the harmonic series:

L = lim(n → ∞) ((n - 1) / (2n - 1)) / (1 / n)

By simplifying this expression, we get:

L = lim(n → ∞) (n - 1) / (2n - 1) * n