A divergent sum?

$\large 1 -2 + 2^2 - 2^3 + 2^4 - \cdots$

The series $\displaystyle \sum_{j=1}^{\infty} a_j$ is said to be Cesàro summable , with Cesaro Sum $A$ , if the average value of its partial sums $\displaystyle s_k=\sum_{j=1}^k a_j$ tends to $A$ , meaning that $\displaystyle A=\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^ns_k$ .

Is the series above Cesàro summable?