Given-that-the-binomial-expansion-of-2-kx-2-5x-2-x-lt-2-5-in-ascending-powers-of-x-is-1-2-7-4-x-Ax-2-find-the-values-of-A-and-k-

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Question Number 66108 by Rio Michael last updated on 09/Aug/19

Given that the binomial expansion of ((2 + kx)/((2−5x)^(2 ) )) , ∣x∣ < (2/(5 )) ,in ascending powers of x is (1/2) + (7/4)x + Ax^2 + ..., find the values of A and k

$${Given}\:{that}\:{the}\:{binomial}\:{expansion}\:{of}\:\frac{\mathrm{2}\:+\:{kx}}{\left(\mathrm{2}−\mathrm{5}{x}\right)^{\mathrm{2}\:} }\:,\:\mid{x}\mid\:<\:\frac{\mathrm{2}}{\mathrm{5}\:}\:,{in}\:{ascending} \\ $$$${powers}\:{of}\:{x}\:{is}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{7}}{\mathrm{4}}{x}\:+\:{Ax}^{\mathrm{2}} \:+\:…,\:{find}\:{the}\:{values}\:{of}\:{A}\:{and}\:{k} \\ $$

Commented by mr W last updated on 09/Aug/19

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Commented by mr W last updated on 09/Aug/19