Write down and simplify the first four terms, in ascending power of $x$, in the expansion of \((8-

Question

Write down and simplify the first four terms, in ascending power of $x$, in the expansion of $(8-9x)^{\frac{1}{3}}$. Hence, by finding a suitable value of $x$, find a rational approximation to $\sqrt[3]{-10}$. Why is this not a good approximation?

Accepted Answer

$ -\frac{65}{32}. $

Example involving Binomial Series

Example involving Binomial Series