P(n) is defined as an n-term product (4-2/1)*(4-2/2)*...*(4-2/n).

Prove P(n) is an integer for all natural numbers n.

(In reply to re: demonstration by Kenny M)

I'm  still not sure I get it.  (2n)!/(n!)^2  divide out n!.  This leaves (n+1)*(n+2)*...2n divided by the remaining n!.  If, for example,  n+7 is prime, the the result cannot be an integer?  Whete am I wrong?

Posted by Kenny M on 2022-05-26 20:20:59