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    Radius of Convergence and Abel's Theorem in Complex Analysis

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    A) I want to prove that if sum of a_n(z-a)^n have radius of convergence 1 and if the sum a_n converges to A then lim (r -> 1- ) of the sum (a_n r^n) = A. ( I believe z here is a complex number).

    B) Using Abel's theorem, prove that log2 = 1 - 1/2 + 1/3 - ...

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    Solution Summary

    Radius of Convergence and Abel's Theorem are investigated. The solution is detailed and well presented.