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.
200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.