Express $\mathrm{f}\left( x \right)=\frac{6{{x}^{3}}+11{{x}^{2}}+2}{\left( {{x}^{2}}+1 \right)\left(

Question

Express $\mathrm{f}\left( x \right)=\frac{6{{x}^{3}}+11{{x}^{2}}+2}{\left( {{x}^{2}}+1 \right)\left( 2x+3 \right)}$ in partial fractions. Hence expand $\mathrm{f}\left( x \right)$ in ascending powers of $x$ up to and including the term in ${{x}^{3}}$, stating the range of values of $x$ for which the expansion is valid. Find the coefficient of ${{x}^{2001}}$ in expansion of $\mathrm{f}\left( x \right)$. [9]

Accepted Answer

$-\left(\frac{2}{3}\right)^{2002}$

JPJC Tutorial Question 10

JPJC Tutorial Question 10

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