Use binomial expansion to show that 1+6x1−4x≈1+5x+152x2\displaystyle \sqrt{\frac{1+6x}{1-4x}} \approx 1 + 5x + \frac{15}{2}x^21−4x1+6x≈1+5x+215x2
A student substitutes x=15\displaystyle x = \frac{1}{5}x=51 into the expansion to find an estimate for 11\sqrt{11}11. Give a reason why the student should not use x=15\displaystyle x = \frac{1}{5}x=51
Substitute x=114\displaystyle x = \frac{1}{14}x=141 into 1+6x1−4x=1+5x+152x2\displaystyle \sqrt{\frac{1+6x}{1-4x}} = 1 + 5x + \frac{15}{2}x^21−4x1+6x=1+5x+215x2 to obtain an approximation for 2\sqrt{2}2. Give your answer as a fraction in its simplest form.
408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.