Unformatted text preview: Exercise 3. Consider the power series expansion 1 12 xx 2 = ∞ X n =0 a n x n . Prove that, for each integer n ≥ 0, there is an integer m such that a 2 n + a 2 n +1 = a m . [Putnam Exam, 1999, A3] Exercise 4. Evaluate lim x → 1∞ Y n =0 ± 1 + x n +1 1 + x n ² x n . [Putnam Exam, 2004, B5]...
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 Fall '10
 RyanDaileda
 Multiplication, Complex number, Putnam Exam

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