Math 2602

March 21 , 2000


Name:____________________________

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:


Express as  a sum of falling factorials.


Use this result to find:

Answer

Problem  2 (10 Points)

Sum by parts:

Answer

Problem 3: (8 points)

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



a)

   
b)  n!

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

c)  

d)

Since = + , we get   for the difference.

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

e) n(n!)

f)