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.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
