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Question
Write the coefficient of the middle term in the expansion of \[\left( 1 + x \right)^{2n}\] .
Solution
\[\text{ Here, n, i . e . , 2n, is an even number . } \]
\[ \therefore \text{ Middle term } = \left( \frac{2n}{2} + 1 \right)\text{ th term } = \left( n + 1 \right)\text{ th term}\]
\[\text{ Thus, we have } : \]
\[ T_{n + 1} =^{2n} C_n \left( 1 \right)^{2n - n} \left( x \right)^n \]
\[ =^{2n} C_n x^n \]
\[\text{ Hence, the coefficient of the middle term is } {}^{2n} C_n \]
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