# Thread: Set Theory

1. ## Set Theory

Hi Can anyone please help me to solve this problem?

List the elements (a1, a2, a3 . . . ) where an is defined as a1 = 1, an = nan-1, n E N, 1 < n < 7.

2. Originally Posted by flwer_13
Hi Can anyone please help me to solve this problem?

List the elements (a1, a2, a3 . . . ) where an is defined as a1 = 1, an = nan-1, n E N, 1 < n < 7.
$a_1=1$
$a_2=2\cdot a_{2-1}=2\cdot{1}=2$
$a_3=3\cdot a_{3-1}=3\cdot 2=6$
$\vdots$
$a_n=n\cdot a_{n-1} =n\cdot(n-1)\cdot a_{n-2}=\cdots=n\cdot(n-1)\cdot(n-2)\cdot(n-3)\cdots1=n!$

3. Thank You!