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

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

  1. A

    anbnba

  2. B

    an+1bn+1ba

  3. C

    bn+1an+1ba

  4. D

    bnanba

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    Solution:

    1(1ax)(1bx)=1a-ba1-ax-b1-bx 1(1ax)(1bx)=aab(1ax)1+bba(1bx)1

    , coefficient of xn is aanab+bbnba=bn+1b-a-an+1b-a

    coefficient of xn=bn+1an+1ba

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