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Question
Find the 4th term from the end in the expansion of \[\left( \frac{4x}{5} - \frac{5}{2x} \right)^8\] .
Solution
Let Tr+1 be the 4th term from the end of the given expression.
Then,
Tr+1 is (10 − 4 + 1)th term, i.e., 7th term, from the beginning.
Thus, we have:
\[T_7 = T_{6 + 1} \]
\[ =^{9}{}{C}_6 \left( \frac{4x}{5} \right)^{9 - 6} \left( \frac{5}{2x} \right)^6 \]
\[ = \frac{9 \times 8 \times 7}{3 \times 2}\left( \frac{64}{125} x^3 \right)\left( \frac{125 \times 125}{64 x^6} \right)\]
\[ = \frac{10500}{x^3}\]
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