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