great! I see that my version of the book is the special indian edition so chapters are mixed up. Now Im only behind a chapter (being sarcastic!)
The questions read as follows:
Find all solutions of the recurrence relation
a -subscript-n = n+2-2a-subscript-n-1, a-subscript 1 = 0
My instructor says it is similar to:
Let R be the relation R-{(a,b) | a divides b} on the set of positive integers. Find
A) r^-1
B)R^-
and
Which of the relations from Example 7 are symmetric and which are antisymmetric?
Do these indeed relate? I've read the entire chapter and haven't seen one problem setup like the one asked.
Not quite.
First find the solution to the homogeneous recursion
The characteristic equation of which is r+2=0, which has root r=-2 (multiplicity 1)
so
Now we need a particular solution. For this problem we look for a solution of the form
plugging it into the recursion we get
equating like terms we get
B = -2B + 1
C = 2B -2C + 2
so B = , and C =
so the general solution is
If the problem had an intial condition, we could solve for A.