series

I am struggling with the mid term approaches. The following are a couple of Series that I am struggling with: Find the domain of convergence of each of the following: a) Summation from n = 1 to infinity of [(z-1)^2n]/((2n)!) b) Summation from n = 1 to infinity of [(n^2 + 1)/(2n + 1)]z^n c) Summation from n = 1 to infinity of [(z + 1)^n]/n d) Summation from n = 0 to infinity of [(z - 1)/(z + 1)]^n I appreciate the help!

trig functions

The trigonometric problems I am having are: a) Solve the equation sin(z) = sqrt(2) b) Show that |Cos(x+iy)|==0 and minus infinity < x < infinity c) Show that |Sinh(z)|^2 = Sinh^2(x) + Sin^2(y) I appreciate the help!

Financial accounting

Poulsbo Manufacturing, Inc. is currently an all-equity firm that pays no taxes. The market value of the firm's equity is $3 million. The cost of this unlevered equity is 15% per annum. Poulsby plans to issue $600,000.00 in debt and use the proceeds to repurchase stock. The cost of debt is 4% semi-annually. A. After Poulsbo repurchases the stock, what will the firm's weighted average cost of capital be. B. After the repurchase, what will the cost of the equity be? Explain. C. Using MM-Proposition 2, what will be the average cost of capital after the repurchase?

Application of Residues

I want to find the Cauchy value by using residues. (See attached file for full problem description)

Evaluating the improper integrals using residues theorem.

Evaluating the improper integrals using residues theorem. See attached file for full problem description.