1. Determine whether or not the alternating series converge or diverge. (a) (-1)' "-1 In(n' +1) (b) [(-1) n- - 2n+2 7n2 -2n+1 2. Determine whether the series converges absolutely, or converges conditionally, or diverges and give reasons for your conclusions. nov3n +1 (6 ) 2 3. Use Ratio Test or Root Test to determine whether the following infinite series are absolutely convergent. (a) (-1)"+1 3" (b) In(n) n 4. Find the interval of convergence for the power series (a) _ n=1 2n+1 n (b) 1=1 5. Use the substitution method and a known power series to find power series for function function Sin(3x) Please express your answer in one sigma notation. X 6. Calculate the Maclaurin series for f (x) = = 1 - to the x3 term. 2+ x