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In the expansion of (x-(3)/(x^(2)))^(30)...

In the expansion of `(x-(3)/(x^(2)))^(30)`, find the `5^(th)` term.

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Verified by Experts

`(r+1)`th term of the expansion of `(x-(3)/(x^(2)))^(30)` is given by
`T_(r+1)=.^(30)C_(r)x^(30-r)((-3)/(x^(2)))^(r)`
We have to find `T_(5)thereforer=4`
`T_(5)=.^(30)C_(4).x^(30-4)(-(3)/(x^(2)))^(4)`
`=(30xx29xx28xx27)/(4xx3x2xx1).x^(26).(3^(4))/(x^(8))`
`=2219805x^(18)`
Hence, `5^(th)` term in the expansion of `(x-(3)/(x^(2)))^(30)` is 2219805`x^(18)`.
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