Definition: A is a rational number which is not 1. We divide 1 by 1 minus a, which is called the difference reciprocal of A. for example, the difference reciprocal of 2 is 1 divided by 1 minus 2 = negative 1, the difference reciprocal of negative 1 is 1 divided by 1 minus bracket minus 1, which is equal to half. It is known that a "1" equals one third, a "2" is the difference reciprocal of a "1", a "3" is the difference reciprocal of a "2" By analogy, then a "2" equals, a "3" equals, a "4" equals, and a "2013" equals

Definition: A is a rational number which is not 1. We divide 1 by 1 minus a, which is called the difference reciprocal of A. for example, the difference reciprocal of 2 is 1 divided by 1 minus 2 = negative 1, the difference reciprocal of negative 1 is 1 divided by 1 minus bracket minus 1, which is equal to half. It is known that a "1" equals one third, a "2" is the difference reciprocal of a "1", a "3" is the difference reciprocal of a "2" By analogy, then a "2" equals, a "3" equals, a "4" equals, and a "2013" equals

a2=3/2,a3=-2,a4=1/3,a2013=-2

Definition: A is a rational number that is not 1. We call 1 minus 1 / 2 as the difference reciprocal of A. for example, the difference reciprocal of 2 is 1 minus 1 / 2
Definition: A is a rational number that is not 1. We call 1 / 1-A the inverse of A. for example, the inverse of 2 is 1 / 1-2 = - 1, the inverse of - 1 is 1 / 1 + 1 = 1 / 2. We know A1 = - 1 / 3, A2 is the inverse of A1, A3 is the inverse of A2, A4 is the inverse of A3,... And so on, what is A2009?
Because I don't quite understand

It is known that A1 = - 1 / 3,
Then A2 = 1 / [1 - (- 1 / 3)] = 1 / (4 / 3) = 3 / 4
a3=1/[1-(3/4)]=1/(1/4)=4
a4=1/(1-4)=-1/3
a5=1/[1-(-1/3)]=1/(4/3)=3/4
a6=1/[1-(3/4)]=1/(1/4)=4
……
It can be seen from the above process that the calculation results are regular, and there will be a cycle after every three times,
2009÷3=669…… two
So A2009 = A2 = 3 / 4

A is a rational number that is not 1. If we divide 1 by 1-A, it is called the reciprocal of difference of A. for example, the reciprocal of difference of 2 is 1 divided by 1-2 = negative one
-If A1 = - 3, what is a2014?

It is known that A1 = - 3, A2 is the reciprocal of difference of A1, A3 is the reciprocal of difference of A2
A1 = - 3; A2 = 1 / 4; A3 = 4 / 3; A4 = - 3 is a sequence of three number cycles
2014=3*671+1;a2014=a1=-3
Just to the first number of a cycle - 3
[think about it, that's the key]

A is a rational number that is not 1. If we divide 1 by 1-A, it is called the difference reciprocal of A. for example, the difference reciprocal of 2 is 1 divided by 1-2 = minus one, A1 = one third, A2 is the difference reciprocal of A1, A3 is the difference reciprocal of A2, A4 is the difference reciprocal of A3, and so on, then A2012 =?

A1 = 1 / 3
A2 = 1 △ 1 / 3 = 3 / 2
A3 = = 1 ÷ (3 / 1-2) = - 2
A4 = 1 △ 1 - (- 2)) = 1 / 3
.
Cycle, cycle 3
therefore
2012÷3=670..2
Namely
A2012 = A2 = 3 / 2

How to calculate 3.9 times 10.3 minus 0.3 times 3.9

Original formula = 3.9 × 10.3-0.3 × 3.9
=3.9×(10.3-0.3)
=3.9×10
=39

5.6 times 3.3 plus 5 and 3 / 5 times 7.7 minus 5.6!

5.6x3.3 + 5 and 3x7.7-5.6
=5.6x3.3+5.6x7.7-5.6
=5.6x(3.3+7.7-1)
=5.6x(11-1)
=5.6x10
=56

How simple is 3-2 of 3 * 21 of 10-7 of 2

3-2 of 3 * 21 of 10-7 of 2
=5 out of 3-7 to 2 out of 7
=3 - (5 / 7 + 2 / 7)
=3-1
=2

Simple operation of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

55

1.5 × (6 + 7.68 △ 3.2) simple calculation

There seems to be no easy way:

2 out of 7 = 6 out of 21 = 18 out of 63 = 4 divided by?
Questions on the paper

It should be four fourths