Define a recursive sequence by a1 1 an nan 1 for n greate

Define a recursive sequence by a_1 = 1, a_n = na_n - 1, for n greaterthanorequalto 2. Describe in words how you could compute n! for any positive integer n.

Solution

a₁=1 , a_n=na_n-1

when n=2

a₂=2a₁=2

when n=3

a₃=3a₂=3*2=6

when n=4

a₄=4a₃=4*6=24

when n=5

a₅=5*24=120

So the sequence is

1,2,6,24,120,...

That is

1!,2!,3!,4!,5!.....n!