Inspired by Pi Han Goh, Part 2

Calculus Level 5


The series above diverges, of course. Its Abel sum is defined as

\[A=\lim_{x\to 1^-}\sum_{n=0}^{\infty}(-1)^{n+1} n x^n\]

Find \(A\) to three significant figures. Enter 666 if you come to the conclusion that no such Abel sum \(A\) exists.

Twin Problem


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