<ol class="i-list"><li><div class="list-item-paragraph">Using standard result given in the List of Formulae (MF26), find the Maclaurin’s series for&nbsp;$\ln (1+x+{{x}^{2}})$, up to and including the term in ${{x}^{3}}$.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Determine the set of values of $x$ for which the expansion in part <strong>(i)</strong> is valid.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Hence, or otherwise, obtain the series expansion of $\frac{1+2x}{1+x+{{x}^{2}}}$ up to and including the term in ${{x}^{2}}$.<span class="inline-marks">[2]</span></div></li></ol>

Using standard result given in the List of Formulae (MF26), find the Maclaurin’s series for $\ln (1+x+{{x}^{2}})$, up to and including the term in ${{x}^{3}}$.

Determine the set of values of $x$ for which the expansion in part **(i)** is valid.

Hence, or otherwise, obtain the series expansion of $\frac{1+2x}{1+x+{{x}^{2}}}$ up to and including the term in ${{x}^{2}}$.

Maclaurin Series and Power Series - Maclaurin Series and Power Series - General

Question 023e840a

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