Find the pattern and fill in the number 2 4 6 10_____ 26______

Find the pattern and fill in the number 2 4 6 10_____ 26______

2 4 6 10__ 16___ 26___ 42___

Given the function f (x) = (x-1) ^ 2, G (x) = 4 (x-1), the sequence an satisfies A1 = 2, and (an + 1-an) g (an) + F (an) = 0
1. Try to explore whether the sequence (an) - 1 is equal ratio sequence
2. Try to prove that ∑ AI > = 1 + n
3. Let BN = 3f (an) - G [a (n + 1)], try to explore whether there are maximum and minimum terms in BN? If so, find out the maximum and minimum terms. If not, explain the reason

1.(a(n+1)-an)4(an-1)+(an-1)²=0
(an-1)(4a(n+1)-4an+an-1)=0
4a(n+1)=3an+1
a(n+1)-1=(3/4)(an-1)
An-1 the first term is 1 and the common ratio is 3 / 4
2.an-1=(3/4)^(n-1)
an=(3/4)^(n-1)+1
sn=(1-(3/4)^n)/(1-3/4)+n
sn=4-4*(3/4)^n+n≥1+n
3.bn=3(an-1)²-4(a(n+1)-1)
a(n+1)-1=3/4*(an-1)
bn=3(an-1)²-3(an-1)
bn=3((an-1)-1/2)²-3/4
bn=3((3/4)^(n-1)-1/2)²-3/4
(3 / 4) ^ (n-1) has no minimum value, and the maximum value is 1. When n = 1, BN has the maximum term, B1 = 0
Only when (3 / 4) ^ (n-1) is closest to 1 / 2, BN has the smallest term
n=2,3/4>1/2,3/4-1/2=1/4
n=3,9/16>1/2,9/16-1/2=1/16
n=4,27/641/16
So when n = 3, BN has the smallest term, B3 = 3 / 256-3 / 4 = - 189 / 256

Let y = f (x) be the solution of the differential equation y "+ y '- e ^ SiNx = 0, and f' (x0) = 0, then whether f (x) has the maximum and minimum at x0 or only increases and decreases

Substitute x0 into the original equation: y '' (x0) = e ^ (sinx0) > 0, so f (x) takes the minimum value at x = x0

Find the rule to fill in the number: 0, - 3,8, - 15,24, (), () to be accurate!

-3548 put aside the negative number first, and then add the negative sign to the odd number

The numerator of a false fraction is 47. When it is transformed into a fraction, the numerator, denominator and integral part are three consecutive natural numbers. What is the false fraction?

The false score is 47 / 6
After the band fraction, it is 7 and 5 / 6
You can set the denominator as X, then the numerator with fraction is (x-1), and the integral part is: (x + 1)
(x+1)×x+(x-1)=47
The solution of the equation is: x = 6
Therefore, the final score is: 7 and 5 / 6, and the false score is: 47 / 6

______ It's a positive number______ Is a negative number______ It's a natural number______ It's an integer

1, 2, 3 are positive numbers, - 3, - 2, - 1 are negative numbers; 0, 1, 2, 3 are natural numbers, - 3, - 2, - 1, 0, 1, 2, 3 are integers. So the answer is: 1, 2, 3; - 3, - 2, - 1; 0, 1, 2, 3; - 3, - 2, - 1, 0, 1, 2, 3

Write 4 / 67, 4 / 15, 16 / 53, 16 / 23, 25 / 39, 64 / 31, (), ()

This is the answer
4/67、4/15、16/53、16/23、25/39、64/31、（ 31/25）、（256/39 ）
It is divided into odd sequence and even sequence
4/67、16/53、25/39、（31/25）
The molecular order is + 12, + 9, + 6
The denominator is - 14
4/15、16/23、64/31、（256/39）
Multiply the molecules by four
Denominator in turn + 8

What is the largest natural number that can be divided by 30 and has 30 positive divisors?

Let P1 ^ A1 * P2 ^ A2 *... * PN ^ an be the prime factor of positive integer decomposition,
Then the number of divisors is (a1 + 1) (A2 + 1) (A3 + 3)... (an + 1)
Because the number required in the question can be divided by 30, there must be prime factors 2,3,5,
Let this number be 2 ^ A1 * 3 ^ A2 * 5 ^ A3
Then its divisor number is (a1 + 1) (A2 + 1) (A3 + 1),
Because 30 = 2 * 3 * 5, this number has no prime factor except 2,3,5, so a1 + 1, A2 + 1, A3 + 1 can only be 2,3,5 or 3,2,5 or 5,2,3 or 5,3,2 or 2,5,3 or 3,5,2, there are 6
Then A1, A2, A3 can only take 1,2,4 or 2,1,4 or 4,1,2 or 4,2,1 or 1,4,2 or 2,4,1
That is, the six natural numbers are
2^1*3^2*5^4=11250
2^2*3^1*5^4=7500
2^4*3^1*5^2=1200
2^4*3^2*5^1=720
2^1*3^4*5^2=4050
2^2*3^4*5^1=1620
So to sum up, the maximum natural number is 11250

How to draw the image of exponential function y = 2-2 Λ x?

The image of y = 2 ^ x is made first, and then the image of y = - 2 ^ x is made
Finally, it is translated upward by two coordinate units, that is, the image of y = 2 - 2 ^ X

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