Observe 1 / 2, 2 / 7, 3 / 14, 4 / 23, 5 / 34. The nth number is ()

Observe 1 / 2, 2 / 7, 3 / 14, 4 / 23, 5 / 34. The nth number is ()

First of all, observe the molecules. As the number of molecules increases, they change in the order of 1, 2 and 3. So the numerator of the nth number is n. then look at the denominator, which are 2, 7, 14, 23 and 34 respectively. It seems that there is no rule. This is that they can be deformed. Generally, the deformation can be all plus or minus a certain number

-1. What is the law of 2, 7, 14, 23, 34? It is expressed by the formula containing n

N^2-2

Observe the characteristics of the following sequence, fill in the blanks with appropriate numbers, and write a general formula
1.（ ）,-4,9,（ ）,25,（ ）,49
Why can't the general term formula be written as (- 1) ^ (n-1) * n ^ 2!

The general formula is as follows:
                   
That is: sign is the law of positive and negative, the number part is the square of positive integer
Do you mean this formula?
               
As long as the value range is clear, it should be no problem
 
 
 

Cyclic sequence 2,5,2,5,2,5 What is the general term formula of?

Solution 1: 2,0,2,0,2,0 The general formula of is an = 1 - (- 1) ^ n
0,5,0,5,0,5… The general formula of is an = 5 [1 + (- 1) ^ n] / 2
2,5,2,5,2,5 can be obtained by adding The general formula of is an = [7 + 3 * (- 1) ^ n] / 2
Solution 2: an = 2|sinn π / 2| + 5|cosn π / 2|

It is known that A1 = 1, & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; an + 1 = (1 / 3) Sn & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; (n = 1.2.3.4.)
Formula for finding general term

If we know A2 = 1 / 3 and Sn = 3A (n + 1), we can change n into n-1, s (n-1) = 3an, guarantee that the subscript is positive, and N ≥ 2, then we can get Sn - S (n-1) = 3A (n + 1) - 3an (n ≥ 2) by subtracting the two formulas

(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?
Simple algorithm

Observation items: 1 / 8 = (1 / 2-1 / 4) / 21 / 24 = (1 / 4-1 / 6) / 21 / 48 = (1 / 6-1 / 8) / 21 / 80 = (1 / 8-1 / 10) / 21 / 120 = (1 / 10-1 / 12) / 21 / 168 = (1 / 12-1 / 14) / 21 / 224 = (1 / 14-1 / 16) / 2, put forward 1 / 2; it is easy to sum in brackets; namely: (1 / 2-1 / 16) * 64 / 2 = 16-2 = 14

Find out the arrangement of the following numbers, and point out what number does the question mark in brackets represent? 42 (44) 38 23) 28 why do you fill in this number?
This problem is very difficult. Can you work it out

42 44 38 23 （22） 28
42+44=86 9^2+5
38+23=61 8^2-3
+28=50 7^2+1
So (?) is 22

（1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/228）*128

（1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288）*128
=（1/2+1/6+1/12+1/20+1/30+1/42+14/56+1/72）*32
=（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）*32
=（1-1/9）*32
=8/9*32
=256/9

What is the number in the observation rule question mark?
（2）——（2）——（4）——（8）——（14）——（26）——（48）——（88）——（?）

Starting from the fourth number, each number is the sum of its first three numbers
So the number in the question mark is 26 + 48 + 88 = 162

1. 5 / 2, 19 / 4, 65 / 8 constitute a sequence, and find the general term formula

【2^(n-1)】²+1
———————— (n≥2）
2^(n-1)