Use binomial expansion to show that 1+4x1−2x≈1+3x+32x2\displaystyle \sqrt{\frac{1+4x}{1-2x}} \approx 1 + 3x + \frac{3}{2}x^21−2x1+4x≈1+3x+23x2
A student substitutes x=13\displaystyle x = \frac{1}{3}x=31 into the expansion to find an estimate for 7\sqrt{7}7. Give a reason why the student should not use x=13\displaystyle x = \frac{1}{3}x=31
Substitute x=110\displaystyle x = \frac{1}{10}x=101 into 1+4x1−2x=1+3x+32x2\displaystyle \sqrt{\frac{1+4x}{1-2x}} = 1 + 3x + \frac{3}{2}x^21−2x1+4x=1+3x+23x2 to obtain an approximation for 7\sqrt{7}7. 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.