The growth rate H(s)H(s)H(s) of a synthetic crystal, where sss is the concentration of an additive, is modeled by the function:
H(s)=9s+4(1−3s)(2+s) H(s) = \frac{9s + 4}{(1 - 3s)(2 + s)} H(s)=(1−3s)(2+s)9s+4Express H(s)H(s)H(s) in partial fractions.
Hence find the binomial series expansion of H(s)H(s)H(s) in ascending powers of sss, up to and including the term in s2s^2s2. Give each coefficient as a simplified fraction.
Determine the range of values of sss for which the expansion in (b)(i) is valid.
