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Find the coefficient of x^(3) in the pow...

Find the coefficient of `x^(3)` in the power series expansion of `(5x+6)/((x+2)(1-x))` specifying the region in which the expansion is valid.

Text Solution

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The correct Answer is:
`:."Coefficient of "x^(3)=-(2)/(3)(-(1)/(8))+(11)/(3)(1)=(2+88)/(24)=(90)/(24)=(15)/(4)`
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Find the coefficient of x^(n) in the power series expansion of (x)/((x-1)^(2)(x-2)) specifying the region in which the expansion is valid.

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Knowledge Check

  • The coefficient of x^(4) in the power series expansion of (x^(2)-1)/((x^(2)+1)(x^(2)+2)) is

    A
    `(15)/(16)`
    B
    `(15)/(4)`
    C
    `-(13)/(8)`
    D
    `(77)/(324)`

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