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Complex Variables Convergence of Summations

A) Prove that sum(z^n/n) converges at every point of the unit circle except z=1 although this power series has R=1.

b) Use partial fractions to determine the following closed expression for
c_n

c_n=((1+sqrt5/2)^n+1 - (1-sqrt5/2)^n+1)/sqrt5

Ps. Here c_n are Fibonacci numbers defined by c_0=1, c_1=1,....
c_n=c_n-1 + c_n-2, for n=2,3.....

Solution Summary

The solution to the following problem is given in detailed in the attached solution file.
Prove that sum(z^n/n) converges at every point of the unit circle except z=1 although this power series has R=1.
Use partial fractions to determine the following closed expression for c_n
c_n=((1+sqrt5/2)^n+1 - (1-sqrt5/2)^n+1)/sqrt5

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