Term of the fibonacci sequence
Prove F(2n) = F(n) ( F(n+1) + F(n-1) ) where F(n) is the nth term of the Fibonacci sequence. For all n<=k, let n=k+1. Use induction to prove the left side is equal to the right side.
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Suppose that G is back at its original level, butMs increases by 200. By how much will Y increase in short-run equilibrium? Determine the multiplier for the money supply?
Find the solution to the linear system of differential equations x'=-y and y'=2x-3y satisfying the initial conditions x(0)=-2 and y(0)=-3
Describe in detail how the interest elasticity of investment affects the level of crowding out. Be sure to explain why this is the case.
Assume A is a 2X2 real matrix with eigenvalue lambda=3i and corresponding eigenvector v={{-1-i},{1}}. Determine a fundamental set (i.e., linearly independent set) of solutions for y'=Ay, where the fundamental set consists entirely of real solution
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Suppose you are considering purchasing a savings bond that will pay $100 in 5 years. The market interest rate currently is 3% per year.
Your savings account will be worth $259,000 on January 1 2015. Every month thereafter, you make a cash contribution of $767 to the account.
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