In a study of harmonic resonances, a physicist models the fundamental dampening constant D D\,D as the term independent of ω \omega\,ω in the binomial expansion of P(ω)=(32ω2−4ω3)10P(\omega) = \left( \dfrac{3}{2}\omega^2 - \dfrac{4}{\omega^3} \right)^{10}P(ω)=(23ω2−ω34)10. Calculate the exact value of DDD.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.