Limit of a complex sequence

Prove that if lim(|c_(n+1)/c_n|) = a>0 then lim(|c_n|^1/n) = a

Radius of convergence

(See attached file for full problem description) --- Find the radius of convergence of the following series...(see attachment for equation) ---

Compute the present value of a $100 cash flow for the following combinations of discount rates and times Compute the future value of a $100 cash flow for the same combinations of rates and times as in problem 1 How long will it take for $400 to grow to $1,000 at the interest rate specified What is the present value of a 3-year annuity of $100 if the discount rate is 6 percent What is the present value of the annuity in (a) if you have to wait 2 years instead of 1 year for the payment stream to start?

Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times: r = 8 percent. t = 10 years. r = 8 percent. t = 20 years. r = 4 percent. t = 10 years. r = 4 percent. t = 20 years. Future Values. Compute the future value of a $100 cash flow for the same combinatio ...continues

Find all positive two digit odd numbers with this property: When the digits are interchanged, the result exceeds the original number by more than 36.

This an example from my text book and it gives the answer as 17,19,27,29,39 and 49 but it doesn't give steps to solve. On other questions I have been able to determine the equation but I can't seem to solve with 2 variables. Problem: Find all positive two digit odd numbers with this property: When the digits are intercha ...continues

Elementary properties of analytic mappings (Complex Analysis): find the fixed points of a dilation, a translation and the inversion on C_infinity

1) Find the fixed points of a dilation, a translation and the inversion on C_infinity. 2) Evaluate the following cross ratio: (2, 1-i,1,1+i)

Mobius transformation (Complex Analysis)

1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D. 2). Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).

Analytic functions as mappings (Complex)

1). Let G be a region and suppose that f : G -> C ( C is complex plane) is analytic such that f(G) is a subset of a circle. Show that f is constant. 2). If Tz = (az + b)/(cz + d), find necessary and sufficient conditions that T(t) = t where t is the unit circle { z: |z| = 1}. My solution for number 2 is : T(t) = t , which ...continues

Let T be a Mobius transformation, T doesn't equal to identity. Show that a Mobius transformation S commutes with T if S and T have the same fixed points.

Let T be a Mobius transformation, T doesn't equal to identity. Show that a Mobius transformation S commutes with T if S and T have the same fixed points.

Line Integral

(See attached file for full problem description with equations and diagram) --- Compute where is a square with side = 4, centered at the origin and traced counterclockwise once ---

Composite Function

(See attached file for full problem description with equations) --- real numbers complex numbers Suppose , are continuous functions with nonvanishing first partial derivatives. Let , Show that . ---