1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+...+1/60+...+59/60 Because n goes from 2 to 60 So the original formula = 1 / 2 + 2 / 2 + 3 / 2 + +59/2 =(1+2+…… +59)/2 ＝（1+59）*59/2/2 =885

Denominator is from 2 to 60, and then add all the items with the same denominator to get 1 / 2 = 1 / 21 / 3 + 2 / 3 = 11 / 4 + 2 / 4 + 3 / 4 = 3 / 21 / 5 + 2 / 5 + 3 / 5 + 4 / 5 = 2 The denominator is 2, and the sum of the molecules = (1 + 2 +...) +59) / 2 molecule 1 + 2 + 3 + +59 is the sum of arithmetic sequence, which can be multiplied by the sum of the first term plus the last term

(1) 60 cm () is 24 cm (2) () 3 / 4 () is 2 / 5

The solution of 60 cm (5 / 2) is 24 cm (2), 3 / 4 (8 / 15) is 2 / 5

The numbers 9, 11, 13, 15, 17 and 19 are written on the blackboard. You can erase any two numbers at a time, and then write the sum of the two numbers minus 1 (for example, you can erase 11 and 19, and then write 29). After several times, there will be only one number left on the blackboard. How much is the remaining number? Try to find all the possible answers and prove that there is no other answer

9 + 11 + 13 + 15 + 17 + 19-5 = 79; a: after five times, there will be only one number left on the blackboard. The remaining number is 79

Take a white solid and divide it into two parts of equal mass. Use one part of solid to react with excessive sodium oxide solution to release gases that can make red litmus test paper blue. These gases just neutralize 30ml of 0.1mol/l sulfuric acid; use another part of solid to react with sufficient hydrochloric acid to release colorless and odorless gases. These gases are passed into excessive clarified lime water to produce 0.4g precipitation
Q 1. Calculate the ratio of anions to cations in this white solid
2. What is the white solid
(the answer to the first question seems to be 2:3)

A part of solid reacts with excessive sodium oxide solution to give off the gas that can make the red litmus test paper turn blue. The gas is NH3
NH4 + + OH - = heating = NH3 (gas) + H2O
These gases just neutralize 30ml 0.1mol/l sulfuric acid;
2NH3+H2SO4=(NH4)2SO4
Then the amount of gas is 30 * 0.1 / 1000 * 2 = 0.006mol
Another part of solid reacts with enough hydrochloric acid to release colorless and odorless gas. These gases are fed into excess clarified lime water to produce 0.4g precipitate
It's CO2
According to CO2 + Ca (OH) 2 = CaCO3 (precipitation) + H2O
So the mole number of CO2 is 0.4/100 = 0.004 mol
The acid radicals that can produce CO2 are
HCO3 - + H + = H2O + CO2 (gas)
CO32 - + 2H + = CO2 (gas) + H2O
1 mol CO2 is obtained per 1 mol HCO3 - or 1 mol CO32 -
Now CO2 is 0.004 mol
So the total anion is 0.004 mol
Therefore, the mass ratio of cation and anion is 0.004:0.006 = 2:3
Because it is divided into two parts of equal mass, the original solid contains 0.012 mol of NH4 +, HCO3 - and CO32 - with a total of 0.008 mol
Because compounds are electrically neutral
Let HCO3 - be xmol and CO32 - be ymol
So x + 2Y = 0.012
x+y=0.008
So x = y = 0.004
Therefore, the original solid mixture was obtained by mixing 0.004 mol NH 4HCO 3 and 0.004 mol (NH 4) 2CO 3

If a parallelogram and a triangle are equal in height and base, their area ratio is 2:1______ ．

Because the area of a triangle with equal base and height is half of that of a parallelogram, the area ratio of a parallelogram and a triangle with equal base and height is 2:1

-6,7, - 11,13 are 24

(13-(-11))*(7+(-6))=24

For the fifth grade 50 off formula calculation problems,

Look it up on the Internet

As shown in the figure, in trapezoidal ABCD, the bisectors of ∠ ABC and ∠ DCB intersect at a point P on the trapezoidal median line EF, pH ⊥ AB at h, if EF = 3, pH = 1, then the area of trapezoidal ABCD is______ ．

Through point P, let Mn ⊥ BC be in M, intersect ad in N, ∵ trapezoid ABCD, EF is the median line, ∵ ad ∥ EF ∥ BC, FD = FC, EF = 12 (AD + BC), ∵ PN: PM = FD: FC, ∵ PN = PM, ∵ Pb is the bisector of ∠ ABC, pH ⊥ AB, ∵ PM = pH = 1, ∵ Mn = 2pm = 2, ∵ s trapezoid ABCD = 12 (AD + BC) · Mn = EF ·

If the equation x2 + MX + M-1 = 0 has a positive root and a negative root, and the absolute value of the negative root is large, then the value range of the real number m is______ ．

From the meaning of x1x2 < 0, X1 + x2 < 0, △ 0, from the relationship between root and coefficient, we can get x1x2 = M-1, X1 + x2 = - m, and △ = M2-4 (m-1), so there are m − 1 < 0, − m < 0, △ = M2 − 4 (m − 1) > 0, the solution is 0 < m < 1. So the answer is 0 < m < 1

Application of surface area of mathematical cylinder
Take a cylinder with a diameter and height of 8 cm at the bottom and press its two ends along the direction parallel to the bottom,
Q: how many square centimetres has the surface area increased?

Saw two sections along the parallel direction of the bottom surface, indicating that two bottom surfaces have been added, and the increased surface area is the area of two bottom surfaces, namely
2×3.14×（8÷2）²
=6.28×16
=100.48 (cm2)

1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+...+1/60+...+59/60 Because n goes from 2 to 60 So the original formula = 1 / 2 + 2 / 2 + 3 / 2 + +59/2 =(1+2+…… +59)/2 ＝（1+59）*59/2/2 =885