UIZ # 7 Problems 1. Determine whether or not the alternating series converge or diverge. (a) ( 1) n 2 n 1 ln( n 1) (b) 2 n 1 n 5n 2 ( 1) n 1 3n 2 2n 1 2. Determine whether the series converges absolutely, or converges conditionally, or diverges and give reasons for your conclusions. (a) ( 1) n 1 n 0 3n 1 (b) n 2 n 1 5 3. Use Ratio Test or Root Test to determine whether the following infinite series are absolutely convergent. (a) n n 1 3 ( 1 ) n3 n 1 (b) n ln( n) n n 2 5. Use the substitution method and a known power series to find power series for function function . Please express your answer in one sigma notation. sin( 3 x) x