(i) Find the binomial expansion of (1+3x)−1(1 + 3x)^{-1}(1+3x)−1 up to and including the term in x2x^2x2.
(ii) Show that the first three terms in the binomial expansion of 15−2x\frac{1}{5 - 2x}5−2x1 form a geometric sequence and state the common ratio.
It is given that 85x(1+3x)(5−2x)≡P5−2x+Q1+3x\frac{85x}{(1 + 3x)(5 - 2x)} \equiv \frac{P}{5 - 2x} + \frac{Q}{1 + 3x}(1+3x)(5−2x)85x≡5−2xP+1+3xQ where PPP and QQQ are integers. Find the value of PPP and the value of QQQ.
(i) In a structural model, the stress SSS on a beam at distance xxx from the support is given by S(x)=17x(1+3x)(5−2x)S(x) = \frac{17x}{(1 + 3x)(5 - 2x)}S(x)=(1+3x)(5−2x)17x. Using your answers to parts (a) and (b), find the binomial expansion of S(x)S(x)S(x) up to and including the term in x2x^2x2.
(ii) Determine the range of values of xxx for which the binomial expansion of S(x)S(x)S(x) is valid.
Practise Edexcel A Level Maths 4.3 Using Partial Fractions with exam-style questions for A Level Maths. 4 questions, matched to the Edexcel A Level Maths (9MA0) 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.