Math 166

Summer 2002

Exam 3

 

  1. (18 pt) Determine if the following sequences converge or diverge.

a)             b)            c) where is the partial sum of a positive term series.

 

  1. (36 pt) Determine if the following series converge.

a)    b)              c)       d)

e)      f)

  1. (15 pt) Suppose that you have an infinite series of the form with partial sums given by

a)      Suppose that you find that  Does the series converge? Why or why not.

b)      Suppose that you find that  Does the series converge? Why or why not.

c)      In both cases above, compute  and justify your answer.

  1. (10 pt) Find the center, radius and interval of convergence of the power series
  2. (8 pt) Find a series for  about the point  What is the radius of convergence of this series?
  3. (15 pt) Consider the function

a)      Show that .

b)      Use this to show that

c)      How many terms do you need to guarantee that the approximation has error less than or equal to .001?

7. (8 pt) Evaluate  with error less that or equal to