Question:
The middle term of $\left(x - \frac{1}{x}\right)^6$ is
The middle term of $\left(x - \frac{1}{x}\right)^6$ is
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For even $n$, the middle term is $\binom{n}{n/2} a^{n/2} b^{n/2}$.
Updated On: May 2, 2026
- $-20$
- $-1$
- $1$
- None of these
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
For $(a+b)^n$, if $n$ is even, there is one middle term: $T_{n/2+1}$.
Step 2: Detailed Explanation:
Here $n=6$ (even), so middle term is $T_4 = \binom{6}{3} (x)^{6-3} \left(-\frac{1}{x}\right)^3 = \binom{6}{3} x^3 \cdot (-1)^3 x^{-3} = 20 \cdot (-1) = -20$.
Step 3: Final Answer:
The middle term is $-20$.
For $(a+b)^n$, if $n$ is even, there is one middle term: $T_{n/2+1}$.
Step 2: Detailed Explanation:
Here $n=6$ (even), so middle term is $T_4 = \binom{6}{3} (x)^{6-3} \left(-\frac{1}{x}\right)^3 = \binom{6}{3} x^3 \cdot (-1)^3 x^{-3} = 20 \cdot (-1) = -20$.
Step 3: Final Answer:
The middle term is $-20$.
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