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Unformatted text preview: a n +1 = √ 3 a n + 4 , a 1 = 5 . Is this sequence convergent? If yes calculate the limit. Proceed along the steps outlined below a) Is this sequence bounded above or below? b) Is this sequence monotone increasing or decreasing? c) Calculate the limit c . d) For which values of n is  ca n  < 106 ? IV: (25 points) Suppose you buy a car and you get a loan over P = $5000 .at an interest rate of 5%, monthly compounded. Suppose that you want to pay back the loan within 3 years with Fxed monthly payments. How big is your monthly payment? ±ill in the following steps: a) Denote the monthly payment by M and set a = 5 / 100. How much do you owe at the end of the Frst month (i.e. after your Frst payment)? b) How much do you owe after the nth month? c) Calculate your monthly payment from the answer in b) (Here you may use a calculator)....
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 Fall '08
 N/A
 Calculus, lim, monthly payment, n→∞ n1/p lim

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