# Inspired by Patrick Corn

Calculus Level 4

$\large 1-2+3-4+5-6+\cdots$

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 $A=\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^ns_k$

Is the series $1-2+3-4+5-6 + \cdots$

Cesàro summable? If so, enter its Cesàro sum $$A$$. If not, enter 666.

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