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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=0: c1=c0

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 ???

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Because the index in C_{n} is related to C_{0} via the formula C_{n}=1/n! C_{0}. It is the over-usage of n that confused you. Perhaps it might hep if you use, say m, and write: C_{m}=1/m! C_{0}.