Math 2602

March 21 , 2000


Don't Panic

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] as  a sum of falling factorials.

Use this result to find:



Problem  2 (10 Points)

Sum by parts:




Problem 3: (8 points)

Find the difference (with respect to n- 1 point each)




b)  n!


Not what I was expecting, but correct.
        (n+1)! - n ! =
   (n+1) n! - n! = n n!

c)  [Graphics:Images/index_gr_13.gif]


d) [Graphics:Images/index_gr_16.gif]


Since [Graphics:Images/index_gr_19.gif] = [Graphics:Images/index_gr_20.gif] + [Graphics:Images/index_gr_21.gif], we get [Graphics:Images/index_gr_22.gif]  for the difference.

Find  an anti -difference: (with respect to n - 2 points each)

e) n(n!)


f) [Graphics:Images/index_gr_24.gif]


Converted by Mathematica      April 26, 2000