Find the first number in the following series. (there may be more than one answer?)

?, 2 ,3 , 8, 30, 144, 840, 5760, 45360...

Multiply 2 by 1,3 by 2,8 by 3,30 by 4,144 by 5,840 by 6,5760 by 7,and 45360 by 8.
2,6,24,120,720,5040,40320,362880.
These are the factorials from 2 to 9,so the formula is y(x)=x!/(x-1) where y(x) is the xth number in the sequence.
The first number must be 1!/(1-1)=1/0=infinity.
1/0 is infinity for these reasons.
Reason A:If 1/x=y,then 1/y=x.
Reason B:When x gets bigger,1/x gets closer to 0.
Because of Reason B,1/infinity=0,and plugging that into Reason A,1/0=infinity.

Posted by Tim Axoy on 2003-03-24 09:31:04