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.
144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.