There is a column of 3 / 2, - 5 / 6, 7 / 12, - 9 / 20, 11 / 30, - 13 / 42 Apply the above rule to calculate the sum of the first 100 numbers

There is a column of 3 / 2, - 5 / 6, 7 / 12, - 9 / 20, 11 / 30, - 13 / 42 Apply the above rule to calculate the sum of the first 100 numbers

The general term is (2n + 1) × (- 1) ^ (n + 1) / (n × (n + 1));
So the item 100 is (2 × 100 + 1) × (- 1) ^ (100 + 1) / 100 × (100 + 1) = - 201 / 10100;
Hello, I'm very happy to answer your questions, skyhunter 002 for you
If there is something you don't understand, you can ask it. If you are satisfied, remember to adopt it
If you have any other questions, please accept this question and send it to me for help
Wish you progress in your study

The number of a column arranged according to a certain rule: 2, - 6,12, - 20,30, - 42 , then its nth number is ()

-The N-1 power of 1 is multiplied by n (n + 1), that is (- 1) ^ (n-1) * n (n + 1)

Simple calculation: 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 + 1 / 72 + 1 / 90

6＝2*3 12＝3*4
So 1 / 6 = 1 / 2 + 1 / 3 1 / 12 = 1 / 3 + 1 / 4
If you go on like this, you can get 2 / 5 of the answer

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=（1-1/2）+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+…… +(1/9-1/10)
=1-1/10
=9/10

Simple calculation of 2 / 1 + 6 / 1 + 12 / 1 + 20 / 1 + 30 / 1 + 42 / 1 + 56 / 1 + 72 / 1 Time is running out, just come to the answer on Monday! We are primary school students. The first step of the teacher's rule is 1x2 + 2x3 + 3x4 + 4x5 + 5x6 + 6x7 + 7x8 + 8x9. It's easy to go to school tomorrow. If there's no answer, I'll die ~ @. @ 5.5

1 / (1 * 2) + 1 / (2 * 3) + 1 / (3 * 4) + 1 / (4 * 5) + 1 / (5 * 6) + 1 / (6 * 7) + 1 / (7 * 8) + 1 / (8 * 9) = (1-1 / 2) + (1 / 2-1 / 3) + (1 / 3-1 / 4) + (1 / 4-1 / 5) + (1 / 5-1 / 6) + (1 / 6-1 / 7) + (1 / 7-1 / 8) + (1 / 8-1 / 9) = 1-1 / 9 = 8 / 9

Simple calculation of 1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 + 1 / 72 + 1 / 90

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10=1-1/10=9/10

There is a column of numbers, arranged according to a certain rule: - 1,2, - 4,8, - 16,32... In which the sum of three consecutive numbers is - 768?

x-2x+4x=-768
3x=-768
x=-256
therefore
The three numbers are - 256512, - 1024

There is a column of numbers, arranged in a certain rule into 1, - 2,4, - 8,16, - 32,..., in which the sum of three adjacent numbers is - 96. What are the three numbers?

Notice that the next number in this column is - 2 times the previous one
If the first number of the three adjacent numbers is x, then the second number is - 2x, and the third number is (- 2) x × (- 2) = 4x
x+(-2x)+4x=-96
It is reduced to 3x = - 96
If x = - 32, then - 2x = 64, 4x = - 128
A: these three numbers are - 32, 64 and - 128

There is a column of numbers, which are arranged in a certain rule into - 1,2, - 4,8, - 16, There is a column of numbers arranged in a certain rule into - 1,2, - 4,8, - 16... Where the sum of the three adjacent numbers It's - 192,

If the three numbers are ABC, then it is c-b-a? You can use the following method to assume these three numbers and bring them in to do it. Is the title wrong? If it is sum, it can be done. As follows: suppose the three numbers are 4m, - 2m, m, then they

There is a column of numbers, arranged according to a certain rule into 1, - 2,4, - 8,16 Given that the sum of the three leading numbers is 288, what are the three numbers respectively?

It is not difficult to see from the meaning of the title that this is an equal ratio sequence with a common ratio of - 2
If the first number is x, then the other two numbers are - 2x, 4x
x-2x+4x=288
X = 96 - 2x = - 192 4x = 384
Then these three numbers are 96, - 192384