(1) Cut a square piece of paper into four small squares with the same size and shape, then cut a small square into four small squares in the same way, then cut a small square into four small squares, and so on.

The tangent is 1 2 3 4 5. ....

Number of squares 4 8 12 16 20 ....

If you cut n times * * * and cut out _ _ _ small squares.

If you cut it 100 times, * * * will cut out _ _ _ small squares.

What other rules can you draw by observing the graph? Please write them on the horizontal line _ _ _ _ _ _ _ _ _ _.

Answer: 4n

100*4=400

(2)2x4=3？ - 1 3x5=4？ - 1 4x6=5？ - 1 ... 10x 12 = 1 1？ - 1

Use a formula containing only one letter to express the rule you guessed: _ _ _ _ _ _ _ _ _ _

Answer: (n- 1)(n+ 1)=n? - 1

(3) There are several figures, the first one has a square, the second one has three squares, the third one has six squares, and the fourth one has ten squares. How many squares does the fifth one have? What about the sixth one? Where is the nth one?

Answer: the fifth: 15, the sixth: 2 1, and the nth: n(n+ 1)/2.

(4)1* 2 * 3 * 4+1= 25 = 5 2 2 * 3 * 4 * 5+1=1=/kloc-0.

Answer: n (n+1) (n+2) (n+3)+1.

=[n(n+3)][(n+ 1)(n+2)]+ 1

=(n？ +3n)[(n？ +3n)+2]+ 1

=(n？ +3n)？ +2(n？ +3n)+ 1

=(n？ +3n+ 1)？

That is, n (n+1) (n+2) (n+3)+1= (n? +3n+ 1)？

(5) 1-2+3-4+5-6+......+99- 100 (2) 1+2-3+4-5+6-......-99+ 100 (3)0-|72/7 1-7 1/72|+|7 1/72-72/7 1|

Answer:-1*50=-50

(6) Observe the following numbers:11,-1/2,-2/1/3,2/2,3/1,-1/0.

Answer: Look at the law:

The denominator is 1, 2 1, 32 1, 432 1, ....

The number of numbers is 1.2340% arithmetic progression, so 1.2345 is already 15, so the next one should be 6, so the denominator should be 6.

The molecular range is from 1,-1 -2, 123,-1 -2 -3 -4, .....

The number of numbers is 1 2 3 4 5 ..., so by 5, the number has reached 16, so the next number should be-1 -2 -3 -4 -5 -6, because even numbers are negative. So the number 16 is:-1/6.

Look at the law again:

1 2 3 4 5 6 7 is 28 at this time, and the number after 5 is the 33rd number. So the denominator should be

8。 The fifth from the bottom, so the denominator should be 4.

Now look at the numerator: when it reaches 8, it is the fifth number, and because the even number is negative, it should be -5, so the 33rd number is -5/4.