Hi! When going through the examples you did in class on differential equations, I came across a question:
For the first example: y'-y=0 , expanding the power series representation of this you get:
n=1: c2= 1/2 c0
n=2: C3= 1/2*1/3* c0
but then your expression for Cn is:
Cn= 1/n! * C0
why is it not Cn= 1/(n+1)! * C0 ???
Because the index in Cn is related to C0 via the formula Cn=1/n! C0. It is the over-usage of n that confused you. Perhaps it might hep if you use, say m, and write: Cm=1/m! C0.