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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.
 Fall '10
 RyanDaileda

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