Question 14
For any real number $a$ and positive integer $k,$ define $$
\binom ak= \frac{\begin{gathered} a(a-1)(a-2)\cdots\\ {}\cdot(a-(k-1)) \end{gathered}} {\begin{gathered} k(k-1)(k-2)\cdots\\ {}\cdot(2)(1) \end{gathered}}.
$$ What is $$
\binom{-\frac12}{100}\div\binom{\frac12}{100}\ ?
$$
\binom ak= \frac{\begin{gathered} a(a-1)(a-2)\cdots\\ {}\cdot(a-(k-1)) \end{gathered}} {\begin{gathered} k(k-1)(k-2)\cdots\\ {}\cdot(2)(1) \end{gathered}}.
$$ What is $$
\binom{-\frac12}{100}\div\binom{\frac12}{100}\ ?
$$