1.

If|x|lt1thenthecoefficientofx ^ 5intheexpansion of(3x ) /((x- 2 ) ( x + 1 ))is

Answer»

` (33 )/(32)`
`- (33 ) /(32 ) `
` (31 ) /(32 ) `
`- (31 ) /( 32 ) `

SOLUTION : ` (3 x )/( (x - 2 )( x + 1 )) `
` = (- 3 ) /(2) x ( 1 +x ) ^(-1 )(1-(x)/(2) ) ^(-1 ) `
`=(-3 ) /(2)x (1- x+x ^ 2-x ^(3 )+x ^ 4.. )(1 +(x ) /(2)+(x ^ 2 ) /(4)+(x ^ 3) /(8)+(x ^ 4 ) /(16 )+... `
`therefore ` COEFFICIENTOF`x ^5`
`=( - 3 ) /(2 ) [ (1)/(16) - (1)/(8)+(1 ) /(4) - (1)/(2)+1 ] `
`= (-3)/(2) [(1 - 2+ 4 - 8 +16 )/(16)] `
`= (-3 )/(2) ((11)/(16)) `
`=(-33)/(32)`


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