# I can't remember all their names!

Calculus Level 5

$\large 1^m - 2^m + 3^m - 4^m + 5^m - \cdots$

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 closed form of the Abel sum of the (divergent) series as shown above can be written as which of the following functions?

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