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Write-down-the-expansion-of-a-cosx-b-1-l-x-and-hence-show-that-cosx-1-x-1-x-x-2-2-x-3-2-13x-4-24-M-m-




Question Number 185450 by Mastermind last updated on 22/Jan/23
Write down the expansion of   (a) cosx (b) (1/(l+x)), and hence show  that ((cosx)/(1+x)) = 1−x+(x^2 /2)−(x^3 /2)+((13x^4 )/(24))+...      M.m
$$\mathrm{Write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{cosx}\:\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{l}+\mathrm{x}},\:\mathrm{and}\:\mathrm{hence}\:\mathrm{show} \\ $$$$\mathrm{that}\:\frac{\mathrm{cosx}}{\mathrm{1}+\mathrm{x}}\:=\:\mathrm{1}−\mathrm{x}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{13x}^{\mathrm{4}} }{\mathrm{24}}+… \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$
Commented by Mastermind last updated on 22/Jan/23
Hi
$$\mathrm{Hi} \\ $$$$ \\ $$

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