A is a rational number which is not 1. We call 1 / 1-A the difference reciprocal of A. given that A1 = - 1 / 3, A2 is the difference reciprocal of A1, A3 is the difference reciprocal of A2, then what is A2009

A is a rational number which is not 1. We call 1 / 1-A the difference reciprocal of A. given that A1 = - 1 / 3, A2 is the difference reciprocal of A1, A3 is the difference reciprocal of A2, then what is A2009

a1=-1/3,a2=3/4,a3=4,a4=-1/3…… It can be found that after the cycle, A2009 = 3 / 4

There is a column of numbers A1, A2, A3,..., an. Starting from the second number, each number is equal to the difference between 1 and the reciprocal of the number in front of it. If A1 = 2, then a2013

a2=1-1/a1=1-1/2=1/2
a3=1-1/a2=1-1/(1/2)=1-2=-1
a4=1-1/a3=1-1/(-1)=1+1=2
a5=1-1/a4=1-1/2=1/2
.
An is about 2,1 / 2, - 1 cycles
2013/3=671
So a = 2013 = - 1

There are a series of A1, A2, A3. An. Starting from the second number, if each number is equal to the difference between 1 and the reciprocal of its previous number, A1 is equal to 2 / 1, then what is a2013 equal to

a1=1/2
a2=1-1/a1=-1
a3=1-(-1/1)=2
a4=1-1/2=1/2
a5=-1
……
That is: every three numbers a cycle (1 / 2, - 1,2,...)
∵2013=3*671+0
Ψ a2013 is equal to A3
a2013=2