using Abel law
?
The 'Abel's test' for the convergence of a series is described here...
Abel's Uniform Convergence Test -- from Wolfram MathWorld
In the case You have proposed we can observe that...
a) the sequence is not 'monotonic decreasing'...
b) the series diverges...
It seems that the result of the Abel's test in this case is negative...
Kind regards
The series you have proposed is the 'powers series'...
(1)
... computed in , i.e. on the circle with center in and radious . It is easy to demonstrate that (1) converges for , i.e. for all points internal to that circle. A general criterion to extablish what happens on the circle of convergence doesn't exist. In this case we can say that the (1) diverges for ... for other points a detailed study is required...
Kind regards