22. (HM20] Try to put yourself in Euler's place, looking for a way to generalize n! to noninteger values of n. Since (n + 1)!! times ((n + 1) + 1)!/(n + 3)! equals (n+1)!! = n + 1, it seems natural that (n + )!! should be approximately Vn. Similarly, (n + })!! should be approximately n. Invent a hypothesis about the ratio of (n + x)!! as n approaches infinity. Is your hypothesis correct when x is an integer? Does it tell anything about the appropriate value of x! when x is not an integer? 22. (HM20] Try to put yourself in Euler's place, looking for a way to generalize n! to noninteger values of n. Since (n + 1)!! times ((n + 1) + 1)!/(n + 3)! equals (n+1)!! = n + 1, it seems natural that (n + )!! should be approximately Vn. Similarly, (n + })!! should be approximately n. Invent a hypothesis about the ratio of (n + x)!! as n approaches infinity. Is your hypothesis correct when x is an integer? Does it tell anything about the appropriate value of x! when x is not an integer