1.8: Past-paper question 7

(a) Expand $\displaystyle (1 + 2x^2)^{-\frac{3}{4}}$ in ascending powers of $\displaystyle x$ up to and including the term in $\displaystyle x^6$

Express each coefficient as an exact fraction in its lowest terms.

(b) Obtain a series expansion for $\displaystyle f(x)$ in ascending powers of $\displaystyle x$ up to and including the term in $\displaystyle x^5$

Give each coefficient in terms of $\displaystyle k$ where appropriate.

The coefficient of the term in $\displaystyle x^5$ is fourteen times the coefficient of the term in $\displaystyle x^2$

(c) Find the value of $\displaystyle k$