I wanted to know about some good, free books on Infinite Series.
Best Answer
Two sources come to mind: first, Knopp's Theory and application of infinite series like user247608 suggested (very cheap), and Pete Clark's free notes which can be found here: http://alpha.math.uga.edu/~pete/3100supp.pdf
Check out Haskell's site on Recursive function theory. That would be a good start, and you'll likely find more references as you look through the table of contents.
You might want to check out Boolos, Burgess, and Jeffrey's Computatibility and Logic. There's a chapter on recursive functions, starting with primitive recursive functions, and a subsequent section on recursive relations. (You can preview the text and its table of contents at the link above to see if it might meet your needs.)
You'll also find a nice pdf/handout (actually, a book chapter) from UPenn: Primitive Recursion
Best Answer
Two sources come to mind: first, Knopp's Theory and application of infinite series like user247608 suggested (very cheap), and Pete Clark's free notes which can be found here: http://alpha.math.uga.edu/~pete/3100supp.pdf