We have to prove that there exists a solution of (20.1) or of (20.1’ ) satisfying given initial conditions, say

Log in to see images!

where we have to bumume that Log in to see images!,

(20.3) Log in to see images!

must hold. Replacing the functions Log in to see images! we obtain three first approximate functions

(20.4) Log in to see images!

If we insert these first approximate functions Log in to see images!th approximate functions

Log in to see images!

We have to prove that when n increases arbitrarily Log in to see images! we obtain from (20.2) and (20.4)

Log in to see images!

similarly, Log in to see images!

and in general

(20.6) Log in to see images!

naw, its this equation (20.6) (and the one above it) that confuses me; im sure why that factorial n! is there, somehow u are able to divide by n but im not sure why