# Abel Summation

Calculus Level 3

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

Define the Abel sum $$\sum\limits_{n=0}^\infty a_n$$ to be $$\displaystyle \lim_{z\to 1^-} \sum_{n=0}^\infty a_nz^n,$$ if that limit exists.

The Abel sum of the (divergent) series as shown above can be written as $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. Find $$a+b$$.

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