The binomial expansion of (3+2x)4(3 + 2x)^4(3+2x)4 is given by
(3+2x)4=A+Bx+216x2+Dx3+16x4 (3 + 2x)^4 = A + Bx + 216x^2 + Dx^3 + 16x^4 (3+2x)4=A+Bx+216x2+Dx3+16x4Find the value of AAA and the value of BBB.
Show that
(3+2x)4−(3−2x)4=Cx+Ex3 (3 + 2x)^4 - (3 - 2x)^4 = Cx + Ex^3 (3+2x)4−(3−2x)4=Cx+Ex3where CCC and EEE are constants to be found.
Hence, or otherwise, find
∫((3+2x)4−(3−2x)4)dx \int \left( (3 + 2x)^4 - (3 - 2x)^4 \right) dx ∫((3+2x)4−(3−2x)4)dx308 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.