# Thread: More Set Theory - HELP

1. ## More Set Theory - HELP

List the elements {a1, a2, a3, ...} where an is defined as a1 =1, an = na n-1, n E N, 1 < n < 7

Out of 2 marks

When n=2, a3 = (2)a 2-1
= (2) (1)
= 2

When n=3, a3 = (3)a 3-1
= (3) (2)
= 6

When n=4, a4 = (4)a 4-1
= (4) (6)
= 24

When n=5, a5 = (5)a 5-1
= (5) (24)
= 120

When n=6, a6 = (6)a 6-1
= (6) (120)
= 720

Therefore the solution set is {2,6,24,120,720} Is this correct?

2. Originally Posted by cnmath16
List the elements {a1, a2, a3, ...} where an is defined as a1 =1, an = na n-1, n E N, 1 < n < 7

Out of 2 marks

When n=2, a3 = (2)a 2-1
= (2) (1)
= 2

When n=3, a3 = (3)a 3-1
= (3) (2)
= 6

When n=4, a4 = (4)a 4-1
= (4) (6)
= 24

When n=5, a5 = (5)a 5-1
= (5) (24)
= 120

When n=6, a6 = (6)a 6-1
= (6) (120)
= 720

Therefore the solution set is {2,6,24,120,720} Is this correct?
If I have read your notation correctly, is this what you mean?
$\displaystyle a_n = n a_{n-1}$ where $\displaystyle a_1 = 1$ and $\displaystyle n \in N$

If so, your answer is correct. You are essentially calculating factorials of integers: each $\displaystyle a_n = n! = n (n-1) ... (2) (1)$