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Question
Find the middle terms(s) in the expansion of:
(ii) \[\left( 1 - 2x + x^2 \right)^n\]
Solution
\[(1 - 2x + x^2 )^n \]
\[ = (1 - x )^{2n} \]
\[\text{ n is an even number } . \]
\[ \therefore \text{ Middle term } = \left( \frac{2n}{2} + 1 \right)th = (n + 1)\text{ th term} \]
\[\text{ Now, we have} \]
\[ T_{n + 1} = ^{2n}{}{C}_n ( - 1 )^n (x )^n \]
\[ = \frac{(2n)!}{(n! )^2}( - 1 )^n x^n\]
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