Find the first three terms, in ascending powers of xxx, of the binomial expansion of
19+x\displaystyle \frac{1}{\sqrt{9 + x}}9+x1
giving each coefficient in its simplest form.
A student wants to use this expansion to obtain an approximation for 3\sqrt{3}3, and notes that each of the three values x=3x = 3x=3, x=−6x = -6x=−6 and x=18x = 18x=18 leads to an expression involving 3\sqrt{3}3.
Without evaluating your expansion, state, giving a reason, which one of the three values of x x\,x should not be used.
Without evaluating your expansion, state, giving a reason, which of the remaining two values of x x\,x would lead to the more accurate approximation.
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.