Find the law, the problem the first year of junior high school has the law exploration question of

Question 1: The first group: their absolute value is their number + 1 squared and the odd number is negative and the even number is positive. The absolute value of n is: (n+1) squared.

The second group: absolute value: 2*1 2*4 2*9 2*16... The second factor is the square of the number of the number. Also, odd numbers are negative, and even numbers are positive. Definitely worth out: 2*(n squared).

Question 2: The 100th of the first group: (100+1) squared = 101 * 101 = 10201

The 100th of the second group: 2 * (100 squared) = 2 * 10000 = 20000 Answer: 10201 * 20000 = 204020000 = 8th power).

Group 1 is 2 squared, 3 squared, and 4 squared......(1)^n（n+1）^2

Group 2 1x2 2x4 3x6 4x8 ...... n x 2n =(-1)^n x 2n^2

So 1 answer is 101 2=10201

2 The answer is 2x100 2=20000

1)1.One positive and one negative, the first number is 2 squared, the second is 3 squared, the third is 4 squared, 5 squared, 6 squared.

1)2.The first number is 2*1, the second is 2*4, the third is 3*6, and the fourth is 4*8....

Ratio size: 4 2+3 2>2x4x3

2)^2+1^2>2x(-2)x1

2^2+2^2=2x2x2

Through observation and induction, write general conclusions that reflect this pattern.

a^2+b^2》2ab

Equal if and only if a=b.

Compare the size of 2008 2007 vs 2007 2008.

Its general form is n n + 1 with (n + 1) n

Compare the size of the two floors of celery in each of the following groups by calculation.

By induction, the magnitude relationship between n n+1 and (n+1) n is .

When n "close brother 2", n n + 1 < (n + 1) n when n > 2, n n + 1 > (n + 1) n

Therefore, the general conclusions obtained in 2008 2007 > 2007 2008 through induction and conjecture are compared with the size of 2008 2007 and 2007 2008.

Ratio size: 4 2+3 2>2x4x3

2)^2+1^2>2x(-2)x1

2^2+2^2=2x2x2

Through observation and induction, write general conclusions that reflect this pattern.

a^2+b^2》2ab

Equal if and only if a=b.

Compare the size of 2008 2007 vs 2007 2008.

Its general form is n n + 1 with (n + 1) n

Compare the size of the two floors in the following groups by calculation.

By induction, the size of n n+1 and (n+1) n is .

When n >> 2, n n + 1 < (n + 1) n

When n >> 2, n n + 1 < (n + 1) n

Therefore, the general conclusions obtained in 2008 2007 > 2007 2008 through induction and conjecture are compared with the size of 2008 2007 and 2007 2008.

(1) n*(-1)^(n+1)

3) No, even numbers in a series are all negative.

Each term is expressed by this equation: (-1) n-1 multiplied by n to denote n-1 is an exponent of -1.

(1) n*(-1)^(n+1)

3) No, even numbers in a series are all negative.

1 2 4 8 16, with a five-pointed star to the power of 2 (n-1) in row n.

3x to the 9th power - 2x to the 5th power.

4x to the power of 13 - 3x to the power of 9.

5x to the power of 17 - 4x to the power of 13.

6x to the power of 21 - 5x to the power of 17.

The nth is (n+2)x to the power (4n+5) - (n+1)x to the power (4n+1).

The number of times is 4n+5

The law of the first sequence is 5=32-22, 12=42-22, 21=52-22, 32=62-22, so the seventh number is =92-22=77, the nth number is =(n+2)2-22, and the small word is 2, squared.

The law of the second series is 12 = 4 3, 25 = 5 5, 42 = 6 7, 63 = 7 9, 88 = 8 11, 117 = 9 13, there are two factors, the following number is the previous factor plus 1, the next factor plus 2, and the two factors are multiplied. Then the 10th number is =13 21=273, and the nth number = (n+3) (2n+1).

45, the nth number is the square of n + 4n;

173,2*(square of n) + 7n+3

9 is 3 squared, 25 is 5 squared, and 49 is 7 squared, which is equivalent to 2n+1, i.e. +1.

4 in 9-1=2*4 equals 2+2

25-1=4*6 in 6 equals 4+2

8 in 49-1=6*8 is equal to 6+2

It's equivalent to 2N, and these questions to find the law are to be done more, and then there will be inspiration, with a sense of number and feeling.