If you look at the number in the following order, you can find out what rule it may be arranged according to which rule you can write three numbers immediately Root number 2, 2, root number 6, root number 2, root number 10___ ,___ ,___ ,.,___ (nth number)

If you look at the number in the following order, you can find out what rule it may be arranged according to which rule you can write three numbers immediately Root number 2, 2, root number 6, root number 2, root number 10___ ,___ ,___ ,.,___ (nth number)

Root 2,2 = root 4, root 6, 2 root 2 = root 8, root 10_ 2 root 3 = root 12__ , Radical 14__ , 4 = radical 16__ ,.,_ Radical 2n__ (nth number)

Give the number of a column arranged in order; - 1,2, - 4,8, - 16,32 1. Write down the three items after 32. 2. According to the law, the nth number is []

-64128, - 256. The second question is (- 1) to the (n-1) power * 2 to the (n-1) power. My mobile phone can't type out the square term, (n-1) is on the upper right of - 1 and 2

There is a column of numbers, arranged in a certain rule into - 1,2, - 4,8, - 16,32. Among them, the sum of three adjacent numbers is 384. What are these three numbers? One more question! A and B start from the starting point at the same time in the 100 meter race. The speed of a is 7 meters per second and that of B is 6.5 meters per second. After 10 seconds of running, because a twisted his foot, the speed is reduced to 6 meters / second. Can b catch up with a before reaching the end of 100 meters Determinant equation

Let these three numbers be x, - 2x, 4x
x-2x+4x=384
3x=384
x=128
Let these three numbers be 128, - 256512
Let B catch up with a in x seconds
Then 7 × 10 + 6 × (X-10) = 6.5x,
70+6x-60=6.5x
0.5x=10
x=20
Because 6.5 × 20 = 130 meters
130 m > 100 m
So B can't catch up with a before reaching the 100 meter finish

There is a column of numbers, arranged according to a certain rule into 1-24-8 16-32. The sum of some three adjacent numbers is 768. What are these three numbers First of all, the law is solved by the method of making equations I cannot understand you

P = (- 1) times the (n-1) power of 2, n = 1,2,3,4`````
(- 1) ^ (n-1) times 2 ^ (n-1) + (- 1) ^ (n) times 2 ^ (n) + (- 1) ^ (n + 1) times 2 ^ (n + 1) = 768
The result shows that n = 9, three numbers are 256, - 5121024

Observe the number in the following column and write the appropriate number 1 / 2, - 3 / 6, 5 / 10, - 7 / 20 on the horizontal line_____ ,_____ . Explain the law!

1/2,-3/6,5/12,-7/20,（9/30）,（-11/42）
Denominator: 1 × 22 × 3 3 × 4 4 × 5 5 × 6 6 × 7 n(n+1)
Molecular: 1 3 5 7 9 11 （2n-1）
Symbol: + - + --

What is the number 2010 What's more, if the number of this column goes down infinitely, which two numbers are getting closer and closer

First, the sign is not considered
You can see that the molecules of fractions are from 1, 2, 3, 4, 5, 6 The denominator is 2, 3, 4, 5, 6, 7 So the number of 2010 is 2010 / 2011. As for the positive and negative sign, we can know that the negative sign corresponds to the odd number on the molecule, so 2010 / 2011 is a positive number
In this infinite arrangement, we can see that the ratio of the difference between the numerator and the denominator is getting smaller and smaller, and finally it will be closer to 1 and - 1

Negative half, two thirds, three quarters, four fifths, five sixths, and seven sixths If the number of this column is infinite, which two numbers are getting closer and closer? Why

-1 and 1
Because 2 * (- 1 / 2) = - 1,3 / 4 * (- 4 / 3) = - 1,5 / 6 * (- 6 / 5) = - 1 and 2 ＞ 3 / 4 ＞ 5 / 6
So it's getting closer to - 1
Because 3 / 2 * 2 / 3 = 1,5 / 4 * 4 / 5 = 1,7 / 6 * 6 / 7 = 1 and 3 / 2 > 5 / 4 > 7 / 6
So it's getting closer to 1

Observe the following number, and then explore the law with your partner: 1, negative half, one third, negative quarter, one fifth, negative six …… (1) Write down the next three numbers; (2) what is the 2009 number? (3) if the column is infinite, which number is closer and closer?

analysis,
1/7,-1/8,1/9
This sequence is
-1/2,1/3,-1/4,1/5,-1/6
Therefore, the nth number is: (- 1) ^ n * 1 / (n + 1)
When n = 2009, (- 1) ^ 2009 / 2010 = - 1 / 2010
If the number is infinite, then the number is infinitely close to zero,
So, this number is very close to zero

People's education press observe the following column number, explore the law. - 1, half, negative one third, one fourth, negative one fifth One sixth. If this column of numbers goes down infinitely, which one is closer and closer to?

-1,1/2,-1/3,1/4,-1/5,1/6,-1/7,1/8,-1/9
Odd number is negative, even number is positive
Infinite row down. Closer and closer to zero

For example, if one-half is reduced by one-third, one-third by one-quarter, by one-fifth by one-sixth, what is the rule?

M sweet dream y,
law:
1/a－1/b＝（b－a）/（a×b）
So:
1/2－1/3＝（3－2）/（2×3）＝1/6
1/3－1/4＝（4－3）/（3×4）＝1/12
1/4－1/5＝（5－4）/（4×5）＝1/20
1/3－1/4＝（6－5）/（5×6）＝1/30