There are 10 law finding questions in 7th grade mathematics

1+1/3，1+10/11，13/15，16/19...is a string of regular numbers, in which the ninth number is ( ) If the denominator of a fraction is 1999, then the numerator of this number is ( ).

There is a kind of game: the rule is: nickname, Xiao Hua two classmates sit back to back, by the name of the left, middle, right three piles of exercise books are a number, Xiao Hua commanded the name from the left, the right two piles respectively to take m, n (a is greater than m, a is greater than n) to the middle pile, and then the middle pile back to the right pile of the remaining 2 copies of the number to the right pile, so far, Xiao Hua can point out the final number of the middle pile.

When m=2n, the final principal number of the middle heap is y, write the functional relationship between y and n, and when a=99, what is the maximum value of y?

1，12，1，1，1，2，……Please write out the following 4 numbers and a string of true scores, arranged in the following way 6...., 1, use the formula with n to represent the law 2, write the 1001st true fraction.

Question 1, (

Question 2, (

Question 3

I can meet you, you don't even type the questions, who will help you find books, and slowly turn over the 10 regular questions.

You give me 200 points, and you haven't said any version yet, Boss, please figure it out before you send it, okay?

1，4，9，16，25...are all squared numbers, i.e. n, and the 100th is 100 = 10000. The 20th is 20 = 400.

2，-8，-18，-32，-50……is -2n and the 20th digit is -2*20 = -800.

1，4，9，16，25……How is the law of this set of numbers expressed, and what are its 100th and 20th numbers?

The n2 20th digit is 20 2=400

The 100th number is 100 2 = 10000

2，-8，-18，-32，-50……How to express the law of this group of numbers, and what is its 20th number?

The 20th digit of 2*n 2 is -2*20 2=-800

The 100th number is -2*100 2=-20000

1 squared, 2 0 squared, 3 squared. The 100th number is 10000 squared by 100, and the 20th number is 20 squared.

The next number is smaller than the previous number, 2+(n-1)*4, and the general formula for the nth term = -2+(-2+(-4))+2+2*(-4))+

There are a total of n-2 in it; The latter can be seen as a series of equal differences, and the formula for summing the first term is 0, the tolerance is -4, and the result is -2*n*(n-1).

Substituting the above equation, the nth term = -2*n + (-2) * n * (n-1) = -2n squared.

1. If all digits are squared, 100 numbers are 10000, and 20 numbers are 400

2. The opposite number of 20 is -400*2=-800

Hope that helps you :)

1 2 2 2 3 2 4 2 5 2 is squared The 100th number 100 2 = 10000 The 20th number 20 2 = 400

Each is n squared, the hundredth is 10,000, and the 20th is 400,

111、、、 Number Arrangement Rules, Number Arrangement Rules, Number Arrangement Rules, Number Arrangement Rules, Number Arrangement Rules, 1. Observe the following equations: 1+3=4=2 squared, 1+3+5=9=3 squared, 1+3+5+7=16=4 squared....According to this law (1) Try to guess: 1 + 3 + 5 + 7 +....The value of +2005+2007 ?

2) Promotion: 1+3+5+7+9+....What is the sum of +2n-1)+(2n+1)? 2. What numbers should be filled in the last two digits of the following number series?

2 3 5 8 12 17 3. 1 1 2 3 5 8 21 4, there is a string of numbers, and its arrangement is 、...Guess what the 100th number is? 5. There is a string of numbers 3 6 10 15 21 What is the 6th number?

6. Observe the arrangement of the following group of numbers 、...Then the 2005th number is ( )a 1 b 2 c 3 d numbers are arranged in a row, in which any three adjacent numbers, the middle number is equal to the sum of the two numbers before and after it, if the first two numbers of these 100 numbers are 1,0 in turn, then the number of "0" in these 100 numbers is 2222、、、 geometric figure change law problem geometric figure change law problem geometric figure change law problem geometric figure change law problem 1. Observe the arrangement of the following balls (where is a solid ball and is a hollow ball):

From the first ball to the 2004th ball, there are solid balls 2, observe the following figure arrangement rules (where is a triangle, is a square, is a circle), if the first figure is a square, then the 2008th figure is (fill in the name of the figure).

The first plus the last term is multiplied by the number of terms divided by 2, which is:

1＋n）×n÷2

an=2n-1

where an denotes the nth phase and n is a positive integer.

, 3/4, 5/9, minus 7/16, 9/25, (nth) 2There is a sheet of paper with a thickness of millimeters, after folding them in half 1 time, the thickness is 2 times the millimeter, and after folding 2 in half, the thickness is ( ) millimeters. Fold in half 20 times thereafter, the thickness is ( ) mm.

After folding in half n times, the thickness is ( ) mm.

3.Knowing that the speed of the ship in the reverse water is m kilometers per hour and the speed of the current is 2 kilometers per hour, then the speed of the ship in still water is ( ) kilometers per hour.

4.Calculate 1 2 3 4 5 ......＋2001－2002＋2003＝（5.A 3-digit number, the 10-digit number is x, the single-digit number is 3 times less than the 10-digit number, and the 100-digit number is 3 times the one-digit number, then the three-digit number can be expressed as ( ).

10*11=11011*11=12112*11=13213*11=14314*11=15415*11=165What is the relationship between the ten digits and the single digit and the hundred digits? ——

A lot of people are stressed out when you play around like this.

There is a body of a drink bottle.

-3-1=-4

And so on, the odd-numbered law is as follows.

1 3 5 7....Get the result -4 -5 -6 -7....One less at a time to learn smaller and smaller.

2nd 4 6 8....Get the result -2 -1 0 1 2....Increase by 1 each time

Therefore, the odd and even numbers move the result of the law separately, the twentieth -2 -1 0 1 even times the tenth -2 + 9 = 7 if s = 64The result must be an even number of -2 + (66) = 64It is also said that the 67th number is 64, and the 67th even number is 134, so after moving 134 times, s = 64

I don't know if the result is right, the analysis process should be very clear, hope to smile and add more points.

Move one unit length to the left minus 1, and move one unit length to the right plus 1 to have, the first time: -3-1=-4

The second time: -3-1+2=-2

The third time: -3-1+2-3=

Nth time: (when n is an odd number), -3-1+2-3+.1) *n (when n is an even number), -3-1+2-3+...

1*n will move this number in two, when n is even, when it is -3+1*n, when 2n is odd, when it is -3+1*(n-1) 2-n has the twentieth time it is -3+10=7

When s=64, it is discussed in two cases, and it can be seen that n is an even number and 134, and n is an odd number, so it is rounded.

-4, -2, 7, -n-2 (n is odd), -3 + n 2 (n is even).

When observing the equation, we can get that n is an odd number, the result must be less than 0, so n is an even number, that is, s=-3+n 2=64, so we get n=134 times.

The nth equation can be obtained as follows: n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, this number is -4, -2, -5, -1, -6, 0, -7, 1, 8, 2That should tell you something. If not, look at n=1,3,5,7,9 and this number is -4,-5,-6,-7,-8

When n=2,4,6,8,10, this number is -2,-1,0,1,2, so it looks good. They are all scattered along -3 to the left and right. So you can get it by giving it a little try.

According to its moving law, sn=-3+(-1) n times n can be obtained

Substitute s=64.

can get n = 67

Remember that the far point is on -3, move the odd number of times the point will be on the left, move the even number point will be on the right, (draw a number line by yourself, and the way of using the column ** is simpler), you will find that from -3 if you start from -3 to the left is -3-4-5-6-7-8, if it is to the right, it is -7-6-5-4-3-2-10, odd means 2n+1, even number means 2n, so the first time this number is -4, the second time this number is -2, After the twentieth time the number is 12, and after n times it will be ...

I haven't found a pattern yet, so I'll wait a minute

-4 -2 7 when n is an even number there is an=-3+n 2 when n is an odd number there is an=-3+n 2 -1

The answer is 128 times.

Divide the former term by 2 and multiply it by (-1) n to get the latter term, and the last two terms are: 1 64, -1 128

The nth term of this sequence is (-1) n*1 (2 n).

1.1 in 64, -1 in 128

2.(-2) to the nth power.

-1 to the nth power of 2, -1 2 when n is odd, -1 8... When n is even, it is 1 4, 1 16...

Each time the denominator is multiplied by 2, the odd number is negative.

The last two answers are 1 in 64 and 1 in 128. The law is -nth power of (-2).

（1+n）*n/2

The nth digit is 1+2+......The sum of n.

You can do the math with a series of equal differences.

If you haven't learned, you can use the following methods to calculate!

1+ 2 +…n-1)+n

n+(n-1)+…2 +1

Just add the above two formulas and divide them by two.

It is understood as: the sum corresponding to the addition of upper and lower numbers is (n+1), there are n such sums, and then divided by 2 is the result of the formula.

Find the law:

The nth number is 1+2+3+4+·· n = n(n+1) 2Note: In the last step, the formula for summing the difference series is used.

Solution: Observations:

The first number is equal to: 1=1

The second digit is equal to: 1+2=3

The third digit is equal to: 1+2+3=6

The fourth digit is equal to: 1 + 2 + 3 + 4 = 10

The nth number is equal to: 1+2+3+4+5... n is calculated to be equal to: [n*(n+1)] 2

Using the squared difference formula, the formula is expressed as: (n+1)*(n+3)=(n+2) 2-1; n denotes the nth sub.

Process: (n+1)*(n+3)=[(n+2)-1]*[n+2)+1]=(n+2) 2-1

(n-10)*(n+1)=n 2-1, which is available in math books, you can take a closer look.