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प्रश्न
Find the coefficient of:
(ii) x7 in the expansion of \[\left( x - \frac{1}{x^2} \right)^{40}\]
उत्तर
(ii) Suppose x7 occurs at the (r + 1) th term in the given expression.
Then, we have:
\[T_{r + 1} = ^{40}{}{C}_r x^{40 - r} \left( \frac{- 1}{x^2} \right)^r \]
`= (-1)^r "^40C_r x^(40-r-2r)`
\[\text{ For this term to contain } x^7 , \text{ we must have: } \]
\[40 - 3r = 7\]
\[ \Rightarrow 3r = 40 - 7 = 33\]
\[ \Rightarrow r = 11\]
\[ \therefore \text{ Coefficient of } x^7 = ( - 1 )^{11} \]` "^40C_11 = "^-40 C_11`
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