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If(x - 4 )/( x^ 2 - 5x+6)canbeexpandedintheascendingpowersofx,thenthe coefficientofx ^ 3is |
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Answer» ` ( - 73 )/(648) ` `=(2 ) /((x - 2 )) - (1)/((x - 3 )) ` `therefore(2) /((x - 2 )) - (1)/((x-3))= (2)/((-2) (1 - (x ) /(2)) )+(1)/(3(1 -(x)/(3)) ` =` (1 ) /(3) (1 -(x )/(3)) ^( -1)- (1 -(x)/(2)) ^(-1) ` `=(1)/(3) [ 1+(x)/(3)+((x)/(3)) ^ 2+ (x/3)^ 3 +... ] ` ` - [ 1+(x )/(2)+ (x/2) ^2+(x/2 ) ^ 3+... ] ` `therefore`CO - efficientof`x ^ 3` inaboveexpansion is ` (1)/(3)(1/3) ^3- (1/2) ^3 = (1)/(81)- (1)/(8)= ( -73)/(648) ` |
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