Mathematics problem solving! Urgent! Detailed problem solving process! 1. Calculate the values of 2,2 + 4,2 + 4 + 6,2 + 4 + 6 + 8 respectively 2. According to the calculation of 1., we guess the expression of 2 + 4 + 6 +... + 2n Prove your conjecture by mathematical induction Can you answer the third question in detail

2 * (1 + 2 + 3... + n) and then use the parity formula to take it

RELATED INFORMATIONS

1. Three math problems, how many can be solved 1. The total weight of the two barrels of oil a and B is 60 kg. The weight ratio of the remaining oil and B is 3:7. How many kg of oil was there in barrel a? 2. To process a batch of parts, the time ratio of a, B and C is 3:4:5? 3. There are three granaries a, B and C, with a total grain weight of 96 tons. If 3 tons are transported from each of the two granaries AB to C, the grain storage ratio of the three granaries is 4:3:1. How many tons of grain were stored in each of the three granaries
2. ① The route from a city to B city is 9750km long. It takes 12.5h for an aircraft to fly from a City downwind to B city, and 13h for it to fly against the wind. The average speed and wind speed of the aircraft can be calculated ② : a unit marches 4 hours a day and 5 hours the next day. It marches 98 km in two days, and the first day is 2 km less than the second day. What is the average speed of the first day and the second day? ③ Objective: to prepare 18kg antiseptic liquid containing 50% medicine with 30% and 75% antiseptic liquid?
3. Yes, I will- 1. A plane flies in the two cities with a wind speed of 24 km / h. It takes 2 hours and 50 minutes to fly along the wind and 3 hours to fly against the wind. The speed of the ball seamless aircraft is the same as the distance between the two cities 2. It takes 3 hours for a ship to go back and forth between wharf A and wharf B. It takes 30 minutes more for a ship to sail upstream than downstream. If the speed of the ship in still water is 26 km / h, calculate the current speed 3. A ship sails downstream from wharf a to wharf B, and then reverses to wharf C for 9 hours. It is known that the speed of the ship in still water is 7.5 km / h, and the water flow speed is 2.5 km / h. If the distance between wharf A and wharf C is 15 km, the distance between wharf A and wharf B is calculated Find the answers to these three questions I hope I can finish it by the end of the evening
4. 1. The lengths of two sides of a triangle are 8cm and 12cm respectively. Find the perimeter of the triangle 2. The length of three sides of an isosceles triangle is 4cm, (3x-2) cm, (x / 2 + 1) cm respectively. Find the value of X and the length of three sides of the isosceles triangle 3. In triangle ABC, ∠ B is 15 ° smaller than ∠ a, and ∠ A is 15 ° smaller than 2 times of ∠ C. calculate the size of each internal angle —— Write the third question clearly, and it's better to solve three questions together
5. Solving three math problems 1. It is known that a and B are opposite to each other, m and N are reciprocal to each other, and C = 2. Find the value of 2A + 2B + Mn / C 2. If a is less than 0, B is less than 0 and a is less than B, try to determine whether the numbers represented by the following expressions are positive or negative? (1)a+b (2)a-b (3)-a-b (4)b-a 3. Given A-3 + B-4 = 0, find the value of a + B / ab
6. [1/3-(-1/9)+5/12]×(-36) 19 and 15 / 16 × (- 8) (1 and 1 / 2) × (- 1 and 1 / 3) × (- 1 and 1 / 4) × 1 and 1 / 5) × (- 1 and 1 / 6) × (- 1 and 1 / 7)
7. 1. There is a group of numbers arranged according to a certain rule. The order is 2, - 5,9, - 14,20, x, 35 Can you find the value of X? What's the value of X? 2. An ant crawls on a straight line of a chessboard, and the right is the positive direction. For the first time, it climbs one unit to the right from point a, for the second time, it climbs two units to the left to point B, and for the third time, it climbs three units to the right to point C In this way, it has been climbing 20 times to A. point. Given that A. point represents - 18, what number does a point represent? 3. Given that the number represented by point a is - 27 and point B is - 15 on the number axis, find the distance between two points ab To solve this problem, several students put forward the following calculation schemes: A: The larger number minus the smaller number, that is - 15 - (- 27) = 12 B: Subtract the larger number from the smaller number, i.e. - 27 - (- 15) = - 12 C: The absolute value of the difference between the preceding number and the following number, that is | - 27 - (- 15) | = 12 D: The absolute value of the difference between the latter and the former, that is | - 15 - (- 27) | = 12 E: Draw the number axis, actually count the number, that is (here is the number axis), the distance is 12 Which plan do you think is not correct, and explain the reason. Can you think of other plans? What else do you think you should pay attention to the distance between the two points of the ball?
8. Finding the minimum value of a2-2a-6 Given that the value of the algebraic formula x2 + y2-14x + 2Y + 50 is 0, find the value of X and y Given x (x + 1) - (x2 + y) = - 3, find the value of x2 + y2-xy ——— two X2 = x square y2 = y square The third problem is known as X (x + 1) - (x2 + y) = - 3 to find (2 / 2 x2 = Y2) - XY
9. Two mathematical problems of probability, When a store holds a celebration activity, customers can randomly select 2 different gifts from the 4 kinds of gifts when their consumption reaches a certain amount. The probability that one of the gifts selected by any two customers has the same variety is zero___ . The startup password of a device is composed of three different numbers from 0 to 9. If the wrong password is input three times in a row, the device will be shut down permanently. The probability that a person who only remembers that the password is composed of three different numbers can start some devices is 0___ .
10. In order to reduce the number of matches, 20 teams are divided into two groups (10 teams in each group) for competition, and the probability of (1) the strongest two teams being divided into different groups and (2) the probability of being divided into the same group is calculated.
11. 1. The number of boys in a class is 5% less than 4, and the number of girls is more than 40%? 2. It takes 6 hours for ship a to travel from the east port to the West Port, and 4 hours for ship B to travel from the West Port to the east port. Now the two ships start from the east port and the West Port at the same time. As a result, they meet at the place 18 kilometers away from the midpoint. How many kilometers is the distance between the east port and the West Port? 3. There are 162 more male workers than female workers in a factory. Now one eleventh of the male workers and 12 female workers are selected to participate in the speech contest. The number of male workers is twice that of female workers. How many female workers are there in this factory? 4. It costs 5.6 yuan to buy three pencils, two erasers and two exercise books in a shop. If it costs 5.9 yuan to buy two pencils, three erasers and three exercise books, how much is each pencil? 5. For a batch of square bricks, if they are put together into a large rectangle with the ratio of length to width of 5:4, the remaining 38 pieces will be left. If they are changed into a large rectangle with the length and width increased by one piece each, the remaining 53 pieces will be left behind. So, how many square bricks are there in total?
12. 1. If a, B, C ∈ R +, a + B + C = 1, then the minimum value of A2 + B2 + C2 is_____________ 2. Let x, y ∈ R +, and X + 4Y = 4, find the maximum value of XY__________ 3. Let a = {(x, y) y ≥ 0.5 X-2}, B = {(x, y) y ≤ - x + B} a ∩ B ≠ & # 61638; (1) The value range of B is________ (2) If (x, y) ∈ a ∩ B, and the maximum value of X + 2Y is 9, then the value of B is_________ All three questions should be explained in detail,
13. Solving three mathematical problems Find the expression of parabola passing through three points (- 2,0), (0, - 3), (2,2) If the intersection coordinates of the parabola and X axis are (- 2,0), (4,0) and pass (- 1,3), the expression of the parabola is determined If the vertex coordinates of a parabola are (- 2, - 3) and pass through points (1,4), find its expression
14. X - 78% x = 2.2 X + 30% x = 26 2X + 78x = 3.3
15. Three math problems, 1. A set of desk and chair is 135 yuan. The price of desk is 125% of the price of chair. How much are the desk and chair? 2. The dance team has 24 fewer people than the chorus team. 60% of the number of the chorus team is the same as that of the dance team. How many people are there in the dance team? 3. For a car, 7% of the price will be increased if it is purchased in installments. If it is purchased in cash, it will be delivered at a "95% discount". Xiao Ming finds that the installment payment is 7200 yuan more than the cash purchase. What is the original price of the car?
16. Please answer three math questions, thank you! 1: The school bought 6 desks and 12 chairs for a total of 1176 yuan. It is known that the price of each desk is equal to that of six chairs. How much is the cost of each desk? 2: After Xiaohong gives Xiaoming 4.8 yuan, Xiaohong's money is 1.2 yuan less than Xiaoming's. how much more is Xiaohong than Xiaoming? 3: Xiaoqiang and Xiaohong are neighbors, and they are in the same school. Xiaohong has to walk 10 minutes to go to school. Xiaoqiang walks 30 meters more every minute than Xiaohong, so it takes 2 minutes less than Xiaohong. Their home is kilometers away from the school
17. 1 when y=___ 3Y ^ 2-2y = 3 2.x^2+px+q=0（p^2-4p≥0） 3.x^2-5x=(x-___ )^2-(____ )^2
18. 1. If {an} is an arithmetic sequence, A3 + a7-a10 = 8, a11-a4 = 4, what is the sum of the first 13 items of the sequence? 2. A has several books, B borrows half and adds one, C borrows half and adds two, D borrows half and adds three, and finally a has two books left. How many books does a have 3. There are two holes a and B on a drum with a volume of 64. Water flows in from hole a and flows out from hole B. if the flow rate through hole a is 3 L / h, what is the flow rate in hole B to ensure that the container can be filled in 96 hours? 4.y=nx／x-n ＝(n×n／x-n)+n
19. At present, 1000 balls are packed into 100 boxes, and the sum of balls in any 10 boxes can not exceed 190, then a box can have at most balls () A. 108 B. 109 C. 118 D. 119
20. 1. A cylindrical bucket without a cover, measured from the inside, has a bottom diameter of 4 decimeters and a height of 6 decimeters. How many square decimeters of iron sheet is needed to make this bucket? The water depth of the bucket is 5 decimeters, and how many kilograms of water are in the bucket? (take 3.14, 1 liter of water weighs 1 kilogram) 2. The distance between a and B is 264 km. A travels 80 km per hour from a to B by bus. B travels 32 km per hour from B to a by motorcycle. When a runs 200 km, he meets B and asks when a starts ahead of B 3. An electronic dictionary is sold in a stationery shop, and the profit is 15 yuan for each one sold. In order to recover the funds as soon as possible, the price of each dictionary is reduced by 3 yuan. When all the dictionaries are sold out, the profit is 864 yuan. How many electronic dictionaries are sold in the stationery shop? I appreciate the disrespect