Final answer:
The series
!(−1)k+1(k3k)](https://img.qammunity.org/2024/formulas/mathematics/college/lxbg2q0k5e8pyplb6u23azi5dc0nx0q347.png)
Step-by-step explanation:
The series

To determine this, we can use the ratio test. Taking the absolute value of the terms of the series, we have

Using the ratio test, we have
equal to ∞, which means the series diverges. However, when we alternate the signs of the terms, the series converges conditionally.