Inspired by Pi Han Goh

Calculus Level 5

\[1^2-2^2+3^2-4^2+\cdots\]

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

\[A=\lim_{x\to 1^-}\sum_{n=0}^{\infty}(-1)^{n+1} n^2 x^n\]

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


Inspiration.

Twin Problem.

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