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Question
Which term is independent of x, in the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9 ?\]
Solution
\[\text{ Suppose } T_{r + 1} \text{ is the term in the given expression that is independent of x } . \]
\[\text{ Thus, we have: }\]
\[ T_{r + 1} =^{9}{}{C}_r x^{9 - r} \left( \frac{- 1}{3 x^2} \right)^r \]
`= ( - 1 )^r "^9 C _r \frac{1}{3^r} x^{9 - r - 2r} `
\[\text{ For this term to be independent of x, we must have } \]
\[9 - 3r = 0\]
\[ \Rightarrow r = 3\]
\[\text{ Hence, the required term is the 4th term } . \]
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