The first three terms, in ascending powers of xxx, of the binomial expansion of (16+5x)12(16 + 5x)^{\frac{1}{2}}(16+5x)21 are given by
(16+5x)12≈a+58x−25512x2 (16 + 5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2 (16+5x)21≈a+85x−51225x2where aaa is a constant.
State the range of values of xxx for which this expansion is valid.
Choose from the options below:
∣x∣<516∣x∣<165∣x∣<4∣x∣<1 |x| < \frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1 ∣x∣<165∣x∣<516∣x∣<4∣x∣<1Find the value of aaa.
Choose from the options below:
14816 1 \quad 4 \quad 8 \quad 16 14816308 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.