Inspired by Pi Han Goh

Calculus Level 5

1222+3242+1^2-2^2+3^2-4^2+\cdots

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

A=limx1n=0(1)n+1n2xnA=\lim_{x\to 1^-}\sum_{n=0}^{\infty}(-1)^{n+1} n^2 x^n

Find AA to three significant figures. Enter 666 if you come to the conclusion that no such Abel sum AA exists.


Inspiration.

Twin Problem.

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