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Coefficient of $x^3$ in $(1+x^2)(1+x)^{100}$

Coefficient of $x^{10}$ in $(1+x)^{10}(1-x)^{10}$

Coefficient of $x^n$ in $\dfrac{2+x}{2-x}$.

Any help on these would be appreciated.

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    It would help if you would tell us what you know and show us what you've tried. Do you know the binomial theorem? Do you see how to use it to expand $(1+x)^{100}$? Etc., etc.2012-03-22
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    For the second one, note that we are looking at $(1-x^2)^{10}$ and use the known expansion of $(1+w)^{10}$. For the third one, rewrite as $\frac{1+x/2}{1-x/2}$ and use the known expansion of $\frac{1}{1-w}$.2012-03-22

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