Math 2602

Feb 29 , 2000

Section -- Circle One:
Alan Michaels
Shuli Fu
Lisa McShine

Open Book and Notes. You have 50 minutes. Carefully explain your proceedures and answers


Problem 1 (10 points)

Sum by converting to a difference equation and solving that difference equation:

[Graphics:Images/index_gr_2.gif]([Graphics:Images/index_gr_3.gif] -  k)


Problem  2 (10 Points)

Consider the  difference equation:

[Graphics:Images/index_gr_6.gif] =  4 [Graphics:Images/index_gr_7.gif]   + [Graphics:Images/index_gr_8.gif]

[Graphics:Images/index_gr_9.gif] = 1

Let n = [Graphics:Images/index_gr_10.gif], and find a difference eqution for [Graphics:Images/index_gr_11.gif] = [Graphics:Images/index_gr_12.gif]. Solve this difference equation
and initial value. Re-express    the answer   in terms of
n and [Graphics:Images/index_gr_13.gif]. [Graphics:Images/index_gr_14.gif]



Problem 3: (8 points)

a)  (2 points each) Find the limits   as n -> ∞:

    is  3/4

   is zero



Converted by Mathematica      February 29, 2000