The structural load L(w)L(w)L(w) of a specific beam under stress is modeled by the function L(w)=(5+3w)(2+kw)4L(w) = (5 + 3w)(2 + kw)^4L(w)=(5+3w)(2+kw)4, where www represents the deflection in millimetres and kkk is a stiffness constant.
Find the first three terms, in ascending powers of www, of the binomial expansion of
(2+kw)4 (2 + kw)^4 (2+kw)4where kkk is a constant. Give each term in its simplest form.
Given that in the expansion of L(w)L(w)L(w) the coefficient of w2w^2w2 is 24, determine the possible values of the stiffness constant kkk.
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.