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1 × 2 / 1 = 1-2 / 1; 2 × 3 / 1 = 2 / 1-3 / 1; 3 × 4 / 1 = 3 / 1-4 / 1 (1) If n is a positive integer, guess 1 / N (n + 1)=_________ (2) Prove the conclusion of your conjecture; (3) Sum: 1 × 2 / 1 + 2 × 3 / 1 + 3 × 4 / 1 + 2011 × 2013 1 / 2
If 1 / N (n + 1) = 1 / n-1 / (n + 1) is proved, the general division will be OK. The third one is to open one by one, 1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 +. Is this my mistake? The last one is 2011 * 2013? If it is 2012 * 2013, then the previous ellipsis will be followed. + 1 / 2011-1 / 2012 + 1 / 2012-1 / 2013, then
(a ^ 2 + 4) ^ 2-16a ^ 2 (factorization) ^ 2 means square
(a^2+4)^2-16a^2
=(a²+4+4a)(a²+4-4a)
=(a+2)²(a-2)²
There are 3500 cases of fruit in the fruit shop, of which apples account for two seventh. Today, a batch of fruit has been brought in. Now the ratio of the total number of apples to the total number of fruits is 3:8. How many are there now
Less fruit
The problem is wrong, no solution
But if we change the title "a batch of fruits are brought in today" to "a batch of apples are brought in today", it will be solved
According to the meaning of the title, the original number of apples is:
3500 * 2 / 7 = 1000 boxes
Suppose there are x boxes of apples in the new fruit
(1000+x)/(3/8)=3500+x
The solution is x = 500
3500 + 500 = 4000 boxes
A: now there are 4000 boxes of fruit
If | 2x + 1 | and [(y + 1) square] are opposite numbers, find the value of (1) 5xy; (2) - (x's Cube) - (Y's 100th power)
[Note: don't miss the minus sign in question (2).]
I typed a wrong letter just now
|2x+1|=0
（y+1）^2=0
X=-1/2 Y=-1
（1）5xy=5/2
(2) -7/8
How many cubic decimeters does 2 cubic decimeters and 30 cubic centimeters equal
2.03 cubic decimeter
The fruit shop brought in some apples and sold 2 / 7 of the total number on the first day and 3 / 8 of the total number on the second day, with a total of 740 apples sold in the two days
Kilogram, how many apples does the fruit shop bring in?
Total: 740 (2 / 7 + 3 / 8) = 1120 kg
If you make a batch of parts, you can finish half of it in 18 days according to the plan. If you work for 3 days, your work efficiency will increase by 1 / 8. How many days will it take
Suppose there are x parts in this batch, then the efficiency of the original plan is x / 2 / 18 = x / 36, and the efficiency after three days is (1 + 1 / 8) * x / 36 = x / 32. In the first three days, 3 * x / 36 = x / 12 needs to be completed, X / 3 - X / 12 = x / 4 needs to be completed, and (x / 4) / (x / 32) = 8 days, so it takes 3 + 8 = 11 days in total
Capacitance and inductance in parallel, how to determine the composition of the circuit is capacitive or inductive
This is related to the frequency of the signal
Suppose the capacitance of the capacitor is C and the inductance of the inductor is L. since the capacitor and the inductor are in parallel, the complex impedance Z of the circuit is expressed as 1 / z = J ω C + 1 / J ω L. it is simplified as Z = J * (ω L / (1 - ω ^ 2lc)). ω ^ 2 represents the square of ω
According to the expression of Z, when ω L / (1 - ω ^ 2lc) is greater than 0, the circuit is inductive; when ω L / (1 - ω ^ 2lc) is less than 0, the circuit is capacitive
The number of students in a class is between 30 and 50. They are divided into 6, 8 and 12 groups. There is one student left. How many students are there in this class?
The number of people reduced by 1 is just a multiple of 6, 8 and 12
The least common multiple of 6,8,12 is 24
So the number of students can be expressed as 24x + 1 (x is a natural number)
Because the number of students is between 30 and 50
So x = 2, the number of students in this class is 24 × 2 + 1 = 49
How to calculate the nth power of matrix?
（1 -2）^3
(3,4) =? Is there a fixed formula? The process of finding the detailed point, thank you! (Note: I will take away the multiplication of three matrices, if it is n multiplication?)
There is no formula. If n-th power is required, the given matrix must be very special. Its n-th power is regular, a bit like a sequence
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