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Let a, b,c be such that 1/((1-x)( 1-2x)(...

Let `a, b,c` be such that `1/((1-x)( 1-2x)(1-3x)) = a/(1-x) + b/(1-2x) + c/(1-3x)` then `a/1 +b/3 + c/5`

A

` (1)/(15) `

B

`(1)/(6) `

C

`(1)/(5) `

D

`(1)/(3) `

Text Solution

Verified by Experts

` ( 1)/((1 - x )(1 - 2x ) (1 - 3x) ) = (a ) /((1-x )) + (b)/(( 1-2x)) + (c )/((1-3x))… (1)`
substituing x = 2 in equation (1)
`(1)/((1 - 2)(1 - 2(2)) (1 - 3(2))) = (a)/((1- 2)) + (b)/((1-2(2))) + (c )/((1-3(2))) `
` rArr (1)/(-15) = - a + (b)/((-3))+ (c )/((-5)) `
` rArr (1)/(15) = (a)/(1) + (b)/(3) + (c )/(5) `
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