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Math Help - Rational Number Proof

  1. #1
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    Rational Number Proof

    Can you help me with this please!

    Thanks
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  2. #2
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    Sep 2009
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    I'll prove b):
    <br />
\begin{aligned}<br />
(-1) f(z) =(-1) (c_0 + c_1 z+ c_2 z^2 + \ldots + & c_k z^k + \ldots)<br />
\\<br />
a_1 z f(z) = a_1 (c_0 z  + c_1 z^2 + \ldots + & c_{k-1} z^k + \ldots)<br />
\\<br />
\vdots \\<br />
a_k z^k f(z) = a_k & (c_0 z^k + \ldots)<br />
\end{aligned}<br />

    If we add all of above equations we'll obtain:
    <br />
\begin{aligned}<br />
& (-1+a_1 z + a_2 z^2 + \ldots + a_k z^k) f(z) = \\<br />
& (- c_0) + (-c_1 + a_1 c_0) z +(-c_2 + a_1 c_1 + a_2 c_0) z^2 + \ldots <br />
\\<br />
& +(-c_{k-1}+ a_1 c_{k-2} + \ldots + a_{k-1} c_0) z^{k-1} <br />
\end{aligned}<br />
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