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 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.