# Infinite series – An absolute and conditional convergence test to an alternating series with an exponential – Exercise 2856

Exercise

Determine if the following series is absolutely convergent, conditionally convergent or divergent.

$$1\cdot \frac{1}{2}-\frac{1}{2}\cdot \frac{1}{2^2}+\frac{1}{3}\cdot\frac{1}{2^3}-\frac{1}{4}\cdot \frac{1}{2^4}...$$