CONVERGENCE CONSIDERATION

n ! z
n
The radius of convergence of the series is the distance to the nearest singularity of (1 + z ) ı . This occurs at
z = − 1. Thus the series converges for |z| < 1. We can corroborate this with the ratio test. We compute the radius of convergence.

24 S. Reich, “A weak convergence theorem for the alternating method with Bregman distances,” in
Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. Kartsatos, Ed., vol.
178 of Lecture Notes in Pure and Applied Mathematics, pp. 313–318, Marcel Dekker, Ne[r]

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Abstract
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is divergent, conditionally convergent or absolutely convergent.
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