Final_exam (1).pdf

# This is the proposition 25 you may use any result

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This is the proposition 2.5, you may use any result mentioned before proposition 2.5. 2

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Introductory Real Analysis Math 327, Summer 2017 University of Washington c 2017, Dr. F. Dos Reis Exercise 2. Find the least upper bound and the greatest lower bound of the set S = n n + 2 , n N and prove that they actually are the least upper bound and the greatest lower bound. 3
Introductory Real Analysis Math 327, Summer 2017 University of Washington c 2017, Dr. F. Dos Reis Exercise 3. Prove using the definition of the limit that lim n →∞ 2 n 2 + 1 ( n + 1) 2 = 2 . You may use the definition of the limit (definition 25) or any result mentioned before defi- nition 25. 4

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Introductory Real Analysis Math 327, Summer 2017 University of Washington c 2017, Dr. F. Dos Reis Exercise 4. Determine if the following series are convergent, divergent, absolutely convergent, conditionally convergent and justify your answers. Several terms may apply 1. X n =1 1 2 n 2 . 2. X n =1 ( - 1) n n 2 + 1 . 5
Introductory Real Analysis Math 327, Summer 2017 University of Washington c 2017, Dr. F. Dos Reis Exercise 5. Given the series of functions f ( x ) = X 0 ( n + 1) x n 1. For which values of x is the series of function convergent. 2. Prove that f is continuous on [-0.5, 05.]. 3. Use the theorem 64 to find an expression of f on [ - 0 . 5 , 0 . 5]. You may use the geometric series X n =0 x n = 1 1 - x 6
• Fall '08
• NAGY,KRISZTINA
• Calculus, Mathematical analysis, Order theory, Introductory Real Analysis

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