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2005_6SummerMT1

# 2005_6SummerMT1 - ﬁnd the sum ∞ X n =1 1 n 2 n Question...

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Last Name Name Student No Department Section Signature : : : : : : : : : : : : : Code Acad.Year Semester Instructors Date Time Duration ATILIM UNIVERSITY Department of Mathematics Calculus II. I. Midterm Math 152 2005-2006 Summer U.Y., E.S. 03.07.2006 10.30 90 minutes 4 Questions on 4 Pages Total 105 Points 1 2 3 4 Question 1 (25 pts.) Find the radius and interval of convergence X n =1 ( x - 5) n 3 n n

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Question 2 (15+15 pts.)(a) Find the function f ( x ) deﬁned by the power series f ( x ) = X n =1 x n n Hint: 1 1 - x = X n =0 x n , | x | < 1 . (b) Using part ( a

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Unformatted text preview: ), ﬁnd the sum ∞ X n =1 1 n 2 n Question 3 (20 pts.) Determine whether or not the series ∞ X n =1 (-1) n +1 1 ln n is absolutely convergent, conditionally convergent or divergent. Question 4 (10+10+10 pts.) Test the following series for convergence. (a) ∞ X n =1 158 n 2 + 2 n 152 n 2 + 1 (b) ∞ X n =1 n 3 / 2-5 n + 2 n 5 / 2 + 6 n + 1 (c) ∞ X n =1 ± n-1 n ¶ n 2...
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2005_6SummerMT1 - ﬁnd the sum ∞ X n =1 1 n 2 n Question...

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