Sum

In the following expansion, find the indicated term.

`(x^2 - 4/(x^3))^11`, 5^{th} term

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#### Solution

Here, a = x^{2} , b = `-(4)/x^3`, n = 11

For 5^{th} term, r = 4

We have, t_{r+1} = ^{n}C_{r} . a^{n–r}.b^{r}

∴ t_{5} = `""^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 × x^{2}

= 84480 x^{2}

∴ 5^{th} term in the expansion of `(x^2 - 4/x^3)^11` is 84480 x^{2}

Concept: General Term in Expansion of (a + b)n

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