Answer
Converges absolutely
Work Step by Step
The series will converge conditionally when it is a convergent series , but the condition is when the series of its absolute value diverges and the series will converge absolutely but the condition is when the series of its absolute value converges.
A geometric series can be convergent when $|r| \lt 1$ and otherwise, it will diverge.
Here, in the problem we have $\sum_{k=1}^{\infty} (-\dfrac{1}{3})^{k}$, with ratio $r=-\dfrac{1}{3} \lt 1$. This implies that the given series is a geometric series and converges as well.
Thus, we can conclude that absolute value of series converges , so the given series converges absolutely.
