Search results with tag "Binomial expansions"
4. Binomial Expansions - University of Leeds
www1.maths.leeds.ac.uk4. Binomial Expansions 4.1. Pascal's riTangle The expansion of (a+x)2 is (a+x)2 = a2 +2ax+x2 Hence, (a+x)3 = (a+x)(a+x)2 = (a+x)(a2 +2ax+x2) = a3 +(1+2)a 2x+(2+1)ax +x 3= a3 +3a2x+3ax2 +x urther,F (a+x)4 = (a+x)(a+x)4 = (a+x)(a3 +3a2x+3ax2 +x3) = a4 +(1+3)a3x+(3+3)a2x2 +(3+1)ax3 +x4 = a4 +4a3x+6a2x2 +4ax3 +x4. In general we see that the coe cients of (a + x)n come from the n-th row of …
AS PURE MATHS REVISION NOTES
www.mathsbox.org.uk11 BINOMIAL EXPANSIONS Permutations and Combinations • The number of ways of arranging n distinct objects in a line is n! = n(n - 1)(n - 2)….3 × 2 × 1 • The number of ways of arranging a selection of r object from n is n P r = ! ( − )!
Applications of Advanced Mathematics (C4)
mei.org.uk2 Section A (36 marks) 1 Fig. 1 shows part of the graph of Fig. 1 Express in the form where and Hence write down the exact coordinates of the turning point P. [6] 2 (i) Given that where A, B and C are constants, find B and C, and show that [4] (ii) Given that x is sufficiently small, find the first three terms of the binomial expansions of and Hence find the first three terms of the expansion ...