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 combinations of rates and times as in problem 1. Number of Periods. How long will it take for $400 to grow to $1,000 at the interest rate specified? 4 percent 8 percent 16 percent Annuity Values. 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 in... click for more

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 interchanged, the result exceeds the original number by more than 36.

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)