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The following question uses Maclaurin series to investigate approximations of mathematical constants and the accuracies of such approximations.

Given |x|<1, find the sum to infinity of the geometric series $1-x^{2}+x^{4}-x^{6}+\ldots$ .

attempt to use $S_{\infty}=\frac{u_{1}}{1-r}$

Note: Allow working with $u_{1}=1$ and $r=-x^{2}$ or $u_{1}=1-x^{2}$ and $r=x^{4}$ .

=\frac{1}{1+x^{2}}

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