COALITION MATH 152, SPRING 1998

              (S. A. Fulling, assisted by Vera Rice)

                             Day 29.T


    1.  The usual paper shuffling:  Old homework, CAPA, lab 
    sheet, study sheet for final exam.   No written homework for 
    next week; acquaint yourself with teammates' CAPAs.  

    2.  Final exam policy:  May bring the series convergence 
    handout!  Establish day and time of review session.

    3.  Vocabulary from the Grabiner article:  Rigorous

    4.  Review basic concepts of sequences and series from last 
    time.

    5.  Again stress the importance of distinguishing DIvergence 
    and CONvergence.  State the p-test and compare/contrast with 
    the results for improper integrals.  Harmonic series 
    diverges.

    6.  Stress the importance of distinguishing the sequence of 
    terms from the sequence of partial sums.

        A.  Recall TWO functions associated with an improper 
        integral:  the integrand and the antiderivative.

        B.  There are TWO sequences associated with an infinite 
        series.

        C.  a_n -> 0 is a necessary but not sufficient condition 
        for convergence.  There are examples of all 3 possible 
        cases of p => q.  (Same is true for improper integrals, 
        provided we assume the integrand has a limit at all at 
        infinity.)

    7.  Go through the series handout as a TEAM ACTIVITY:
        Each team should study its problem from Sec. 10.7.  
        Choose or solicit examples of all the convergence tests.
THERE WAS NOT AS MUCH TIME FOR THIS AS I HAD HOPED.  WE HAD TWO 
VOLUNTEER PERFORMANCES AND THREE (NOT TERRIBLY SUCCESSFUL) 
COMMAND PERFORMANCES.