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Question
In the following expansion, find the indicated term.
`(x^2 - 4/(x^3))^11`, 5th term
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Solution
Here, a = x2 , b = `-(4)/x^3`, n = 11
For 5th term, r = 4
We have, tr+1 = nCr . an–r.br
∴ t5 = `""^11"C"_4(x^2)^(11 - 4).(-(4)/x^3)^4`
= `(11!)/(4!7!)(x^2)^7.(-(4)/x^3)^4`
= `(11 xx 10 xx 9 xx 8)/(4 xx 3 xx 2 xx 1) xx x^14 xx 256/x^12`
= 330 × 256 × x2
= 84480 x2
∴ 5th term in the expansion of `(x^2 - 4/x^3)^11` is 84480 x2
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