How to prove that not all series have general term formula

How to prove that not all series have general term formula

Just construct a counterexample,
For example, the series composed of the insufficient approximate value of π:
3.1, 3.14, 3.141. There is no general formula

Proving the general term formula of sequence an
The sum of the first n terms of sequence an is Sn A1 = 1 a (n + 1) = Sn + 2 N, which belongs to positive integer

A (n + 1) = Sn + 2, so:
An = s (n-1) + 2
A (n + 1) - an = an. So: a (n + 1) = 2An. This is an equal ratio sequence with a common ratio of 2. A1 = 1
an=1*2^(n-1)=2^(n-1).

Party A and Party B took out the same amount of money and bought a box of apples together. Party A took 12 kilograms and Party B took 18 kilograms. As a result, Party B gave party a 6 yuan and the apples were more than RMB per kilogram
Formula!

(12 + 18) △ 2 = 15kg
Per kilogram: 6 ÷ (18-15) = 2 yuan

If z = y + 3i1 + Xi (x, y ∈ R, I is an imaginary unit) is a real number, then the value of real number XY is ()
A. 3B. -3C. 0D. 3

The solution ∵ z = y + 3i1 + xi = (y + 3I) (1 − XI) (1 + XI) (1 − XI) = (y + 3x) + (3 − XY) I1 + X2 is a real number, and the imaginary part 3 − xy1 + x2 = 0, ∵ xy = 3

A and B race along the playground. It is known that a circle of the playground is 400 meters. A's speed is 100 meters per minute, and B's speed is 80 meters per minute
1) If two people start from the same place and direction at the same time, how often do they meet? (2) if two people start from the same place and opposite direction at the same time, how often do they meet? Please write down your ideas and answers

(1) : when two people start at the same place and direction at the same time, when two people meet, a makes one more circle than B, so it takes 400 / (100-80) = 20 minutes
(2) : if two people start at the same time on the same ground in opposite directions, the sum of speed is 180 meters, and the time is 400 / 180 = 2 / 2 / 9 hours

Tana = root 3 / 2, calculate 1-sin2a / cosa under root

(1-sin2a) / COA = (1-2sinacosa) / cosa = (Sina ^ 2 + cosa ^ 2-2sinacosa) / cosa = (Sina + COSA) ^ 2 / cosa, because Tana = √ 3 / 2 = Sina / cosa and the square of sina + the square of cosa = 1, Sina = √ 21 / 7, cosa = 2 √ 21 / 7, then (1-2sina * COSA) / C

The two trains left the two cities at the same time, traveling for 2.4 hours. The distance between the two trains is 40% of the whole journey. It is known that the speed of car a is 1 / 5 faster than that of car B,
How long is the railway between the two cities?

Speed of car a: 45 × (1 + 1 / 5) = 45 × 1.2 = 54 (km)
The 2.4-hour journey of a and B is the whole journey: 1-40% = 60%
The 2.4-hour journey of a and B is as follows:
（54+45）×2.4
＝99×2.4
= 237.6 (km)
The length of the railway between the two cities is:
237.6 △ 60% = 396 (km)
The formula is as follows:
45×（2＋1/5）×2.4÷（1－40%）
＝99×2.2×2.4÷60%
＝99×2.4÷60%
＝237.6÷60%
= 396 (km)

It is known that 40% of a's weight is equal to 2 / 3 of B's weight, and 3 / 7 of a's weight is 3 / 2kg less than 3 / 4 of B's weight

Let a weigh X and B weigh y
40%x=2y/3
3x/7+3/2=3y/4
From the first formula, we get y = 3x / 5
Substituting into the second formula
x=70
y=42

A certain type of aircraft is trained to fly at a speed of 1200 m / h and 1500 m / h back to the airport. The fuel in the fuel tank of the aircraft can only be used
A certain kind of aircraft is trained to fly at a speed of 1200 m / h and 1500 m / h back to the airport. The fuel in the fuel tank of the aircraft can only maintain a flight time of 2.5 hours. What are the conditions for the flight distance of the aircraft to ensure safety

Let the flight distance be X,
According to the meaning of the title: X △ 1200 + X △ 1500

Given that positive numbers x and y satisfy 2x + 3Y = 4, find the minimum value of 2 / x + 1 / y, and find the corresponding value of X and y at this time

2X + 3Y = 44 (2 / x + 1 / y) = (2x + 3Y) (2 / x + 1 / y) = 4 + 2x / y + 6y / x + 3 = 7 + 2x / y + 6y / X2X / Y > 0,6y / x > 0, so 2x / Y + 6y / x > = 2 √ (2x / y * 6y / x) = 4 √ 3 when 2x / y = 6y / x, take the equal sign x = √ 3y2x + 3Y = 4, so y = (8 √ 3-12) / 3x = 8-4 √ 3, then 4 (2 / X + 1 / y) > = 7 + 4 √ 3, so when x = 8-4 √ 3, y