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Question-103700




Question Number 103700 by anonymous last updated on 16/Jul/20
Commented by anonymous last updated on 16/Jul/20
plzz help me
$${plzz}\:{help}\:{me} \\ $$
Answered by bobhans last updated on 17/Jul/20
(x+(2/x))^8  = (((x^2 +2)^8 )/x^8 ) = ((Σ_(n = 0) ^8 C _n^8  x^(2n) . 2^(8−n) )/x^8 )  = ((2^8 +8×2^7 x^2 +28×2^6 x^4 +56×2^5 x^6 +...)/x^8 )  = ((256)/x^8 ) + ((1024)/x^6 ) + ((28×64)/x^4 ) + ((56+32)/x^2 ) + ...
$$\left({x}+\frac{\mathrm{2}}{{x}}\right)^{\mathrm{8}} \:=\:\frac{\left({x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{8}} }{{x}^{\mathrm{8}} }\:=\:\frac{\underset{{n}\:=\:\mathrm{0}} {\overset{\mathrm{8}} {\sum}}{C}\:_{{n}} ^{\mathrm{8}} \:{x}^{\mathrm{2}{n}} .\:\mathrm{2}^{\mathrm{8}−{n}} }{{x}^{\mathrm{8}} } \\ $$$$=\:\frac{\mathrm{2}^{\mathrm{8}} +\mathrm{8}×\mathrm{2}^{\mathrm{7}} {x}^{\mathrm{2}} +\mathrm{28}×\mathrm{2}^{\mathrm{6}} {x}^{\mathrm{4}} +\mathrm{56}×\mathrm{2}^{\mathrm{5}} {x}^{\mathrm{6}} +…}{{x}^{\mathrm{8}} } \\ $$$$=\:\frac{\mathrm{256}}{{x}^{\mathrm{8}} }\:+\:\frac{\mathrm{1024}}{{x}^{\mathrm{6}} }\:+\:\frac{\mathrm{28}×\mathrm{64}}{{x}^{\mathrm{4}} }\:+\:\frac{\mathrm{56}+\mathrm{32}}{{x}^{\mathrm{2}} }\:+\:…\: \\ $$

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