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Show that coefficient of x^(-3) in the e...

Show that coefficient of `x^(-3)` in the expansion of `(x-1/x)^(11) is -330`.

Text Solution

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`T_(r+1) = (-1)^(r) * . ^(11)C_(r)x^((11-1)) * (1/x)^(r) = (-1)^(r) *.^(11)C_(r)x^((11-2r)).`
Now `11- 2r = - 3 rArr 2r = 14 rArr r = 7.`
`T_(8) = (-1)^(7)*.^(11)C_(7) x^(-3) = -.^(11) C _(4)x^(-3) = - ( 11 xx 10 xx 9 xx 8)/(4 xx 3 xx 2 xx 1) x^(-3) = -330x^(-3).`
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