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1−2+3−4+5−6+⋯1-2+3-4+5-6+\cdots1−2+3−4+5−6+⋯
Define the Abel sum ∑n=0∞an\sum\limits_{n=0}^\infty a_n n=0∑∞an to be limz→1−∑n=0∞anzn, \displaystyle \lim_{z\to 1^-} \sum_{n=0}^\infty a_nz^n, z→1−limn=0∑∞anzn, if that limit exists.
The Abel sum of the (divergent) series as shown above can be written as ab \frac{a}{b}ba, where a aa and b b b are coprime positive integers. Find a+b a+ba+b.
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