According to the regular number: 2, - 4,8, - 16,32, - 64, in which the sum of some four adjacent numbers is - 640, what is the difference between the maximum number and the minimum number If you use X to solve the problem, what's the law? Find x first

According to the regular number: 2, - 4,8, - 16,32, - 64, in which the sum of some four adjacent numbers is - 640, what is the difference between the maximum number and the minimum number If you use X to solve the problem, what's the law? Find x first

X=(-1)^n*2^n
Let the first number be X
Then x * (1-2 + 4-8) = 640
So x = 128
The four numbers are 128, - 256512, - 1024
So the difference between the largest and the smallest of the four numbers is 512 + 1024 = 1536

Observe the number of the following column: 1 / 2, - 1 / 6,1 / 12, - 1 / 20?

We observe molecules 1, - 1,1, - 1. So (- 1) ^ (n + 1)
Denominator 2 = 1 * 2,6 = 2 * 3,12 = 3 * 4,20 = 4 * 5. So n * (n + 1)
Observe the general term of this column number: (- 1) ^ (n + 1) / N * (n + 1)
When n = 8, (- 1) ^ (8 + 1) / 8 * (8 + 1) = - 1 / 72

Look at the following column of numbers: 1 / 2, 1 / 6, 1 / 12, 1 / 20... What is the ninth number?

The rule is that the denominator is n (n + 1), so the ninth number is 1 / (9 × 10) = 1 / 90

One half, one sixth, one twelfth, one twentieth... What's the ninth number, the fourteenth number
If n is an integer greater than 1, write the nth number according to the above arrangement. 18. The altitude of Mount Everest is 8848
m. The altitude of Turpan is - 155m. What's the difference between them?

The ninth number is 1 / (9 × 10) = 1 / 90
The 14th number is - 1 / (14 × 15) = - 1 / 210

One column of numbers: one half, one sixth, one twelfth, one twentieth, one thirtieth?

1/（25×26）=1/650

A column of numbers: half, one sixth, one twelfth, one twentieth, one thirtieth. Find the sum of the first 30 numbers in this column

The 30th is 1 / 30 × 31;
Sum = 1 / 1 × 2 + 1 / 2 × 3 +... + 1 / 30 × 31
=1-1/2+1/2-1/3+...+1/30-1/31
=1-1/31
=30/31;
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Observe half, one sixth, one twelfth, one twentieth, one thirtieth The 60th number is ()

1/3660

What's the rule for half, one sixth, one twelfth, one twentieth

1/(1*2)
1/(2*3)
1/(3*4)
1/(4*5)
.
.
.
a(n)=1/(n*(n+1))

Observe the following numbers, find out the rules and fill in the blanks. What are the 10th and 15th numbers

The tenth is 1 / 110
The 15th is - 1 / 240
The rule is one of n * (n + 1), the odd number is negative, and the even number is positive

One half, one fifth, one tenth, one seventeenth,

1 / 2 / 5 / 10 / 17 (1 / 26) (1 / 37)
5-2 = 3
10-5 = 5
17 -10 = 7
26-17 = 9
37 - 26 = 11