The middle term in the expansion of (1-1x)^n(1-x)^n in powers of x is:

Question

The middle term in the expansion of $\left(1-\dfrac1x\right)^n(1-x)^n$ in powers of $x$ is:

Accepted Answer

$$\left(1-\frac1x\right)^n(1-x)^n=\left(\frac{x-1}{x}\right)^n(1-x)^n=(-1)^nx^{-n}(1-x)^{2n}$$

This has $2n+1$ terms (always odd since $2n$ is even), so the middle term is the $(n+1)$th term, and it works out to

${}^{2n}C_n$

Solutions · 1