1.

For|x|lt1,theconstantterm intheexpansionof(1)/((x -1) ^ 2 (x - 2 ))is

Answer»

` 2`
`1`
`0`
` -(1)/(2)`

SOLUTION : ` (1 ) /((X - 1 ) ^2(x - 2 )) `
`= ( x - 1 ) ^( - 2 )( x- 2 ) ^( -1) `
`= ( - 1) ^( -2)[ ( 1 - x) ^( -2) ] ( -2) ^( -1) [ ( 1 - (x)/(2) ) ^( -1) ]`
`=( -1 ) /(2)( 1 -x ) ^( -2)(1 -(x ) /(2)) ^(-1) `
`=(-1)/(2) [ 1+ 2X+ 3x ^ 2+ ....][ 1+(x )/(2)+ (x ^ 2 ) /(4)+(x ^ 3 )/(8)+ ... ] `
`therefore ` constant term intheaboveexpansionis ` (-1)/(2) `


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