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Question
Find the middle terms(s) in the expansion of:
(i) \[\left( x - \frac{1}{x} \right)^{10}\]
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Solution
(i) \[\left( x - \frac{1}{x} \right)^{10} \]
\[\text{ Here, n is an even number } . \]
\[ \therefore \text{ Middle term } = \left( \frac{10}{2} + 1 \right) \text{ th = 6th term } \]
\[\text{ Now, we have } \]
\[ T_6 = T_{5 + 1} \]
\[ =^{10}{}{C}_5 x^{10 - 5} \left( \frac{- 1}{x} \right)^5 \]
\[ = - \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2}\]
\[ = - 252\]
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