Given that r is a positive integer and f(r) = \frac{1}{r!}, show that f(r) - f(r + 1) = \frac{r}{(r + 1)!}.
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Practise this question^n\mathrm{C}_r and ^n\mathrm{C}_{r-1} in terms of factorials, prove that ^n\mathrm{C}_r + {}^n\mathrm{C}_{r-1} = {}^{n+1}\mathrm{C}_r.[6 marks]S_n = \sum_{r=1}^{n} \frac{r}{(r + 1)!}.[5 marks]S_n in (ii) b) above.[2 marks]f(x) = x^3 - 6x + 4 has a root x in the closed interval [0, 1].[5 marks]0.6 as a first approximation of x_1 in the interval [0, 1], use the Newton-Raphson method to obtain a second approximation x_2 in the…[4 marks]More practice: the rest of this paper · more Series questions · all CAPE Pure Mathematics Unit 2 past papers