Let the first term of sequence {an} be A1 = a ≠ 1 / 4, and a (n + 1) = 1 / 2 * an (when n is even) or an + 1 / 4 (when n is odd) Note BN = a (2n-1) - 1 / 4, n = 1, 2, 3 (1) Find A2, A3 (2), judge whether {BN} is an equal ratio sequence, and prove your conclusion

Let the first term of sequence {an} be A1 = a ≠ 1 / 4, and a (n + 1) = 1 / 2 * an (when n is even) or an + 1 / 4 (when n is odd) Note BN = a (2n-1) - 1 / 4, n = 1, 2, 3 (1) Find A2, A3 (2), judge whether {BN} is an equal ratio sequence, and prove your conclusion

1) Find A2 and A3
A2=A1+1/4=A+1/4
A3=1/2A2=1/2A+1/8
2）B（n+1）/Bn
=[A（2n+1）-1/4]/[A（2n-1）-1/4]
=（1/2*A2n-1/4）/[1/2*A(2n-2)-1/4]
=（A2n-1/2）/[A(2n-2)-1/2]
=[A(2n-1)+1/4-1/2]/[A(2n-3)+1/4-1/2]
=[A(2n-1)-1/4]/[A(2n-3)-1/4]
=Bn/B(n-1)
Because B (n + 1) / BN = BN / b (n-1), and B1 = a3-1 / 4 = 1 / 2a-1 / 8 ≠ 0
So BN is an equal ratio sequence

The package of natural numbers does not include fractions and decimals

Of course not

What is the definition of natural number?
Is there a zero?
What does the high school curriculum say?

The revised set of natural numbers before 0 is a set of positive integers, so there should be 0

Is 0 a natural number?
Do negative numbers have parity?

Whether "0" is included in natural numbers is controversial. Some people think that natural numbers are positive integers, that is, counting from 1; others think that natural numbers are non negative integers, that is, counting from 0. At present, there is no consensus on this issue. However, in number theory, the former is often used; in set theory, the latter is often used!
0 is an even number (according to the International Mathematical Association in 2002, zero is an even number. China also stipulates that zero is an even number in 2004)

It's meaningless to divide natural number by zero, isn't it?

No, it's meaningless to divide a natural number by 0. 0 divided by any number is equal to 0. But 0 can't be a divisor, only a divisor

Is it right or wrong for a nonzero natural number to be inversely proportional to its reciprocal

Yes
Let a nonzero natural number be x, then its reciprocal is 1 / X (x ≠ 0)
X·1/X =1
So, the product of a nonzero natural number and its reciprocal is always 1
That is, a nonzero natural number is inversely proportional to its reciprocal

The reciprocal of nonzero natural numbers is less than 1___ (judge right or wrong)

The reciprocal of 1 is equal to 1 itself, so it is wrong to say that the reciprocal of non-zero natural numbers is less than 1

There is a non-zero natural number. If 3 is used to remove less 1, if 5 is used to remove less 3, if 7 is used to remove less 5, what is the minimum natural number?
We need formulas, not equations

Obviously this number plus 2 can be divided by 3, 5, 7
So the minimum number is 3x5x7 - 2 = 103

() is the factor of all nonzero natural numbers
A. 1B. 2C. 3

From the analysis, we can see that: 1 is the factor of all non-zero natural numbers, so we choose: a

The common factor of all non-zero natural numbers is______ ．

The common factor of all non-zero natural numbers is 1