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Question
Find the middle term in the expansion of:
(i) \[\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}\]
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Solution
(i) Here,
n = 20 (Even number)
Therefore, the middle term is the \[\left( \frac{n}{2} + 1 \right)\] th term, i.e., the 11th term.
\[ T_{11} = T_{10 + 1} \]
\[ = ^{20}{}{C}_{10} \left( \frac{2}{3}x \right)^{20 - 10} \left( \frac{3}{2x} \right)^{10} \]
\[ = ^{20}{}{C}_{10} \frac{2^{10}}{3^{10}} \times \frac{3^{10}}{2^{10}} x^{10 - 10} \]
\[ =^{20}{}{C}_{10}\]
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