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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