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Question
Find the 5th term from the end in the expansion of \[\left( 3x - \frac{1}{x^2} \right)^{10}\]
Solution
Given: \[\left( 3x - \frac{1}{x^2} \right)^{10}\]
Clearly, the expression has 6 terms.
The 5th term from the end is the (11 − 5 + 1)th, i.e., 7th, term from the beginning.
Thus, we have: \[T_7 = T_{6 + 1} \]
\[ =^{10}{}{C}_6 (3x )^{10 - 6} \left( \frac{- 1}{x^2} \right)^6 \]
\[ =^{10}{}{C}_6 \left( 3^4 \right)\left( x^4 \right)\left( \frac{1}{x^{12}} \right)\]
\[ = \frac{10 \times 9 \times 8 \times 7 \times 81}{4 \times 3 \times 2 \times 1 \times x^8} = \frac{17010}{x^8}\]
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