handout1 - Putnam Exam Seminar Fall 2010 Handout September...

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Unformatted text preview: Putnam Exam Seminar Fall 2010 Handout September 27 Exercise 1. Define a sequence {an } recursively by setting a0 = 1, a1 = 2010 and an+1 = Ban − an−1 for n ≥ 1. Determine the value of B so that √ an+1 = 3 + 2 2. lim n→∞ an Exercise 2. Determine the exact value of {xn } if x0 = 0, x1 = 1 and xn+1 = 2xn + xn−1 for n ≥ 1. Exercise 3. Determine if the series 1+ 1 19 2! +2 27 3 19 7 2 + 3! 43 19 7 3 + 4! 54 19 7 4 + ··· converges or diverges. Exercise 4. Show that the series 1+ 1 111111 ++++++ + ··· , 2 3 4 6 8 9 12 whose terms are the reciprocals of the integers that have no prime factors larger than 3, converges, and determine its sum. ...
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This note was uploaded on 02/29/2012 for the course MATH 1190 taught by Professor Ryandaileda during the Fall '10 term at Trinity University.

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