Find the first four terms, in ascending powers of xxx, of the binomial expansion of
(3−13x)5 \left(3 - \frac{1}{3}x\right)^5 (3−31x)5Given that xxx is small, so terms in x4x^4x4 and higher powers of xxx may be ignored, show
(3−13x)5+(3+13x)5=a+bx2 \left(3 - \frac{1}{3}x\right)^5 + \left(3 + \frac{1}{3}x\right)^5 = a + bx^2 (3−31x)5+(3+31x)5=a+bx2where aaa and bbb are constants to be found.
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.