Use binomial expansion to show that 1+3x−32x2≈1+5x1−x\displaystyle 1 + 3x - \frac{3}{2}x^2 \approx \sqrt{\frac{1+5x}{1-x}}1+3x−23x2≈1−x1+5x
A student substitutes x=12\displaystyle x = \frac{1}{2}x=21 into the expansion to find an estimate for 7\sqrt{7}7. Give a reason why the student should not use x=12\displaystyle x = \frac{1}{2}x=21
Substitute x=19\displaystyle x = \frac{1}{9}x=91 into 1+5x1−x=1+3x−32x2\displaystyle \sqrt{\frac{1+5x}{1-x}} = 1 + 3x - \frac{3}{2}x^21−x1+5x=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.