Question

The middle term of $\left(x - \frac{1}{x}\right)^6$ is

• A. $-20$
• B. $-1$
• C. $1$
• D. None of these

Hint:

For even $n$, the middle term is $\binom{n}{n/2} a^{n/2} b^{n/2}$.

Answer 1

The Correct Option is A

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 $-20$.