The strength of a magnetic field BBB, measured in microteslas, at a distance rrr cm from a specific electronic component is modeled by the function:
B(r)=(10r+3)(1−14r)12,0≤r<4 B(r) = (10r + 3)\left(1 - \frac{1}{4}r\right)^{12}, \quad 0 \le r < 4 B(r)=(10r+3)(1−41r)12,0≤r<4Find the first four terms, in ascending powers of rrr, of the binomial expansion of
(1−14r)12 \left(1 - \frac{1}{4}r\right)^{12} (1−41r)12giving each term in simplest form.
Hence determine the coefficient of r3r^3r3 in the expansion of B(r)B(r)B(r), giving the answer in simplest form.
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.