Binomial Theorem

1 - x + x^2 - x^3 + \dots

The expansion of $(1 + x)^{-1}$ is $1 - x + x^2 - x^3 + \dots$ for $|x| < 1$.

False

The expansion has $n + 1$ terms, not $n$ terms.

6

${}^4C_2 = \frac{4!}{2!2!} = 6$.

4th and 5th terms

For odd $n = 7$, there are two middle terms: $\left(\frac{7+1}{2}\right)$th and $\left(\frac{7+3}{2}\right)$th, i.e., 4th and 5th terms.