# A divergent sum?

Calculus Level 4

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

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?

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