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Find the coefficient of x^(-25) in the e...

Find the coefficient of `x^(-25)` in the expansion of `((x^(2))/(2)-(3)/(x^(3)))^(15)`

Text Solution

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The correct Answer is:
N/a

`T_(r+1)=^(15)C_(r)((x^(2))/(2))^(15-r)(-(3)/(x^3))^(t)`
`=^(15)C_(r).(x^(30-2r))/(2^(15-r)).((-3)^(r))/(x^(3r))`
`=^(15)C_(r).((-3)^(r))/(2^(15-r)).x^(30-5r)`
Let 30-5r =- 25
`rArr " "-5r=-55`
`rArr" "r=11`
`:.` coefficient of `x^(-25)=^(15)C_(11).((-3)^(11))/(2^(4))`
`=(-12xx13xx14xx15)/(1xx2xx3xx4)xx(3^(11))/(16)`
`=-(1365)/(16)xx3^(11)`
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Knowledge Check

  • The coefficient of x^(4) in the expansion of ((x)/(2)- (3)/(x^(2)))^(10) is

    A
    `(305)/(256)`
    B
    `(405)/(256)`
    C
    `(504)/(256)`
    D
    0
  • Find the coefficient of x^(4) in the expansion of (2x^(2)+(3)/(x^(3)))^(7)

    A
    `""^(7)C_(2)2^(5)3^(3)`
    B
    `""^(7)C_(2)2^(5)3^(2)`
    C
    `""^(7)C_(2)3^(5)2^(2)`
    D
    `""^(7)C_(2)2^(5)3^(2)`
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