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How do you start expanding this function $$f(z)= \frac{1}{1+\sqrt{2-z}}$$ into two Taylor expansions about $z=0$?

The best I came up is to let $u=\sqrt{2-z}$ and then expand $f(z)$ as a geometric series.

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    What do you mean with "two" Taylor expansions?2011-11-25
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    Did you consider multiplying numerator and denominator by the conjugate of the denominator?2011-11-25
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    Your idea cannot work directly because for the geometric series $u$ has to be small, but if $z$ is small, $u$ isn't.2011-11-25

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