sign (or type) your name below the following honor pledge: I have completed this quiz by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name _____________________ Date___________________ QUIZ # 7 Problems Math 141/6380, Due 11:59PM, Thursday, March 3, 2016 1. Determine whether or not the alternating series converge or diverge. (a) ( 1) n 1 n ln n 1 1 (b) ( 1) n n 1 2n 2 n 2 5n 2 2n 1 2. Determine whether the series converges absolutely, or converges conditionally, or diverges and give reasons for your conclusions. (a) ( 1) n n 3n 4 1 (b) ( 0.2) n n 1 3. Use Ratio Test or Root Test to determine whether the following infinite series are absolutely convergent. (a) 2n ( 1) n 1 2 n n 1 (b) 2 ln n n 2 n 4. Calculate the Maclaurin series for 1 f ( x) 2x to the term. x3 5. Find the interval of convergence for the power series (a) 1 x n 1 n 2n 1 1 (b) n n x n n 2 1 6. Use substitution method and a known power series to find power series for . Please express your answer in sigma notation. f ( x) x cos(3 x )