Question 171
For a positive integer $n$, let $a_n = \frac{(2n)!}{(n!)^3}$. Here $k! = 1 \times 2 \times 3 \times \cdots \times k$.
(1)
Prove $a_n \gt a_{n+1}$ for all $n \ge 3$.
(2)
Find all $n$ such that $a_n$ is a whole number.
(1)
Prove $a_n \gt a_{n+1}$ for all $n \ge 3$.
(2)
Find all $n$ such that $a_n$ is a whole number.