I have to use Cauchy's Double Series Theorem and the following equation,(adsbygoogle = window.adsbygoogle || []).push({});

1/(1-z)^2= 1 + 2z + 3z^2 + 4z^3 + 5z^4+...

to prove that

z/(1+z) - 2z^2/(1 + z^2) + 3z^3/(1+z^3)-+...=

z/(1+z)^2 - z^2/(1+z^2)^2 + z^3/(1+z^3)^2-+...

Any hints on how to start?

Note, |z|<1

(I am not sure, but I think it might be easiest to prove this true where z is real, and then use the identity theorem to show this is true where z is complex)

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# Application of Cauchy's Double Series Theorem

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