find the 2 missing patterns
1,2,6,24,120,..
2,4,8,16,32,..
1,1/4,1/9,1/16,1/25,..
1,1/2,1/3,1/4,..
Your question does not make sense to me.
You have written four series of numbers that could each be expressed as a formula for the nth term, but they have little in common. Many others such series could be written