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## Homework Statement

http://img62.imageshack.us/img62/3433/questionl.png [Broken]

## The Attempt at a Solution

Can anyone help me with this induction?

If [itex]P(z)=Q(z)[/itex] for all [itex]z[/itex] then setting [itex]z=0[/itex] shows that [itex]a_0 = b_0[/itex] .

We must also have [itex]P'(z)=Q'(z)[/itex] and again setting [itex]z=0[/itex] shows that [itex]a_1 = b_1[/itex]

Now I want to show, by induction that each successive derivative, at [itex]z= 0[/itex], gives the equality of the next coefficients.

Do I say that [itex]P^n(0) = Q^m(0) \Rightarrow a_ n = b_m[/itex]

and then [itex]P^{n+1}(z) = Q^{m+1}(z) \Rightarrow 0 = 0[/itex] ??? In particular I need to show that [itex]m=n[/itex] .

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