sequence of partial sums proof

Suppose a_k is a nonincreasing sequence satisfying a_k --> 0 as k--> infinity. Also suppose the sequence of partial sums by s_n = l summation k = 1 to n of b_kl is bounded. Show that these conditions imply summation k = 1 to n of a_k*b_k is convergent.

Financial Accounting

Leases R Us, Inc. has been contracted by Robotics of Beverly Hills to provide a machine that would assist in automating a large part of their current assembly line. Annual lease payments will start at the begining of each year. The purchase price of this machine is $200,000 and it will be leased by RBH for 5 years. LRU will utilize straight line depreciation of $40,000 per year with a zero book salvage value. However, salvage value is estimated to actually be $35,000 at the end of 5 years. LRU is required to earn a 14%, after-tax rate of return on the lease. LRU uses a marginal tax rate of 40%. Calculate the annual lease payments. (Remember, these payments are to be considered at the be... click for more

Bounded linear operator

(See attached file for full problem description with symbols and equations) --- 11.8 Let and where a "1" appears in the n-th position and a zero in all other positions. Let ( ) be a sequence of complex numbers. Prove then that (i) defines a bounded linear operator on G if and only if , and accordingly find the norm of T. (ii) What are the necessary and sufficient conditions for T to be bounded invertible? ---

Showing T is a BLO

(See attached file for full problem description)

This is a financial management problem

1) I wish to purchase a 20 year bond that has a maturity value of $1000 and makes semiannual interest payments of $40. I require a 10 percent nominal yield to maturity on this investment, what is the maximum price I should be willing to pay for the bond? 2)A bond with a face value of $1000 matures in 12 years and has a 9 percent semiannual coupon. The bond has a nominal yield to maturity of 7.5 percent, and it can be called in 4 years at a call price of $ 1045. What is the bond's nominal yield to call?