The concentration C C\,C of a specific reagent in a chemical solution depends on the temperature fluctuation τ\tauτ (in degrees Celsius). For small fluctuations near a reference point, the relationship is modeled by the function:
C(τ)=(5−25τ)7 C(\tau) = \left(5 - \frac{2}{5}\tau\right)^7 C(τ)=(5−52τ)7Find the first four terms, in ascending powers of τ\tauτ, of the binomial expansion of C(τ)C(\tau)C(τ). Give each coefficient as an integer.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.