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Show that the coefficient of x^(4) in th...

Show that the coefficient of `x^(4)` in the expansion of `(x/2-3/x^(2))^(10) "is" 405/256.`

Text Solution

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`T_(r+1) = (-1)^(r)*.^(10)C_(r)*(x/2)^((10 - r)) xx (3/(x^(2)))^(r) = (-1)^(r)*.^(10)C_(r) * 3^(r)*2^(r-10) *x^(( 10 - 3r))`.
Putting ` 10 - 3r = 4, " we get " 3r = 6 rArr r = 2.`
`T_(3) = T_(2+1) = (-1)^(2)*.^(10)C_(2) xx 3^(2) xx 2^(-8) xx x^(4) = 405/256x^(4).`
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