Question

Test the following Alternating Series, if convergent state whether Conditionally or Absolutely.

a) ₁∑[infinity] (−1)ⁿ ln ((4n+3)/(3n+3))

Answer 1

To test the given alternating series, we can use the Alternating Series Test. The series is absolutely convergent.

Step-by-step explanation:

To test the convergence of the given alternating series, we can use the Alternating Series Test. The series is of the form ∑((-1)^n) * ln((4n+3)/(3n+3)).

1. First, we check if the terms of the series approach zero as n approaches infinity. In this case, the limit of the terms does approach zero.

2. Next, we check if the terms of the series are decreasing. To do this, we can take the derivative of ln((4n+3)/(3n+3)). After simplifying, we find that the derivative is negative, indicating that the terms are decreasing.

Since the series satisfies both conditions of the Alternating Series Test, we can conclude that the given alternating series is absolutely convergent.