If the expansion in powers of x of the function $$1(1$$−$$ax)(1$$−$$bx)$$ is $$a0+a1x+a2x2+a3x3+$$…then αnis

Correct option is 3bn+1−an+1b−a

Questions

If the expansion in powers of x of the function $\frac{1}{(1 - ax) (1 - bx)} is a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots$ then $α_{n}$ is

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an−bnb−a

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bn−anb−a

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detailed solution

Correct option is C

∵ (1−ax)−1(1−bx)−1=1+ax+a2x2+…1+bx+b2x2+…∴ an= coefficient of xn in (1−ax)−1(1−bx)−1=a0bn+abn−1+…+anb0=a0bn1+ab+ab2+…=a0bnabn+1−1ab−1=bnan+1−bn+1a−b⋅bbn+1=an+1−bn+1a−b

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If the expansion in powers of x of the function 1(1−ax)(1−bx) is a0+a1x+a2x2+a3x3+…then αnis

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If the expansion in powers of x of the function $\frac{1}{(1 - ax) (1 - bx)} is a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots$ then $α_{n}$ is