Find the first four terms, in ascending powers of xxx, of the binomial expansion of 1+6x\sqrt{1 + 6x}1+6x, giving each term in its simplest form.
Explain how you could use x=112\displaystyle x = \frac{1}{12}x=121 in your expansion to find an approximation for 6\sqrt{6}6. There is no need to carry out the calculation.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.