Look at the number in a column - one third, one eighth, one fifteenth, one twenty-four, one thirty-five. What is the seventh number? What is the tenth number?

Look at the number in a column - one third, one eighth, one fifteenth, one twenty-four, one thirty-five. What is the seventh number? What is the tenth number?

1/3,1/(1×3)
1/8,1/(2×4)
1/15,1/(3×5)
1/24,1/(4×6)
1/35,1/(5×7)
The next item is
1/48 1/(6×8)
The seventh number is
1/63 1/(7×9)
The nth number is
1/(N×(N+2))
The tenth number is
1/120

One third plus one eighth plus one fifteen Add one hundred and twenty to get the final number

First find the general term: an = 1 / (n * n + 2 * n)
a1=1/3;
The last term, n = 10;
The change general term an = 1 / [n * (n + 2)] = 0.5 * (1 / N - 1 / (n + 2));
Summation, term by term cancellation
sn=0.5*(1/1+1/2-1/11-1/12 );

1 / 1 / 2 / 3 / 5 / 8 / 21 / fill in the numbers regularly

one-thirteenth

|- 7 and 1 / 8 - 4 and 1 / 3 | (minus 17 and 1 / 4) | - 2 - 1 / 3| |- 7 and 1 / 8 - 4 and 1 / 3 | + (minus 17 and 1 / 4) + - 2-1 / 3|

|-7 and 1 / 8 - 4 and 1 / 3 | = | - 11 and 11 / 24 | = 11 and 11 / 24
(-69/4)
|-2-1 / 3 | = | - 2 and 1 / 3 | = 2 and 1 / 3

|How to calculate minus 7 and 1 / 8 - 4 and 1 / 3 | (minus 17 and 1 / 4) | - 2 - 1 / 3 |? |- 7 and 1 / 8 - 4 and 1 / 3 | + (minus 17 and 1 / 4) + - 2-1 / 3|

Minus seven and one eighth = - 7-1 / 8 four and one third = 4 + 1 / 3 minus 17 and one fourth = - 17-1 / 4 one third = 1 / 3
So the original formula = | - 7-1 / 8-4-1 / 3 | + (- 17-1 / 4) + | - 2-1 / 3|
=(7+4-17+2)+(1/8+1/3-1/4+1/3)
=-4+13/24
=-3 and 11 / 24

Fill in 1, 4, 2, 1 / 2, 1 / 2, 1 / 4, 1 / 2, 1 / 8, 1 / 32, 1 / 4, 1 / 4, 1 / 4, 1 / 2, 1 / 2, 1 / 2, 1 / 4, 1 / 8, 1 / 2, 1 / 4, 1 / 2, 1 / 2, 1 / 4, 1 / 2, 1 / 2, 1. 4, 2, half, quarter,, (), (), () 2. One eighth, one thirty second, one fourth, one sixteenth, (), (), () 3. One half, one sixth, one twelfth, one twentieth, one thirtieth, one forty second, (). () ()

Question 1: 4, 2, 1 / 2, 1 / 4, (1 / 2), (2), (4)
Question 2: 1 / 8, 1 / 32, 1 / 4, 1 / 16, (2), (1 / 2), (4)
Question 3: 1 / 2, 1 / 6, 1 / 12, 1 / 20, 1 / 30, 1 / 42, (1 / 56), (1 / 72), (1 / 90)

Fill in the numbers regularly. Minus one, one half, one fourth, one eighth (write the 12th number)

-1 1 / 2 - 1 / 4 1 / 8 the twelfth 1 / 2048

Find the rule 1, 1 / 2, 1 / 4, 1 / 8, 1 / 16. What is the 100th number in this row?

Equal sequence: 1 / 2 ^ (n-1)
For example, the first number is 1 / 0 of 2 and the second is 1 / 1 of 2
So the 100th number is 1 / 2 ^ 99

Find the law: (4) (2) (1) (half) () (1 / 8)

Fill in 1 / 4 in brackets. The rule is to start with the first number and multiply each number by 1 / 2
This is a typical sequence of proportional numbers

Observe the number of columns: 3, 8, 15, 24 According to this rule, the 99th number is

Add 1 to each number to get a new sequence
4,9,16,25…… I.e. 2, 3, 4, 5
In this way, the original sequence can be written as 2? - 1,3? - 1,4? - 1,5? - 1 n²-1
The 99th number is 99? - 1 = 9800