If cN0 + 1 / 2cn1 + 1 / 3cn2 +... + 1 / (n + 1) CNN = 31 / (n + 1), find the term with the largest coefficient in the expansion of (1-2x) 2n. (C is followed by two terms.)

If cN0 + 1 / 2cn1 + 1 / 3cn2 +... + 1 / (n + 1) CNN = 31 / (n + 1), find the term with the largest coefficient in the expansion of (1-2x) 2n. (C is followed by two terms.)

Obviously, you ask for what n is
n=4
Then, we can use the formula to get the coefficient of the largest term
2n=8
I forgot that formula
So it's up to you

What is the cubic power of 53 plus the cubic power of 47?

a^3+b^3=(a+b)(a^2-ab+b^2)=(a+b)(a^+2ab+b^2-3ab)
=(a+b)^3*(a+b)-3(a+b)*a*b
53^3+47^3=(53+47)^3-3*(53+47)*53*47
=1000000-3*100*53*47
=1000000-300*(50+3)(50-3)
=1000000-300(2500-9)
=1000000-750000+2700
=250000+2700=252700

The sum of three consecutive even numbers is 30 greater than the largest one. What are the three even numbers?
It doesn't have to be a hard equation, OK

Let the middle of three consecutive even numbers be x, then the largest number is x + 2, and the sum of three even numbers is 3x
3x-(x+2)=30
3x-x-2=30
2x=30+2
x=16
16+2=18
16-2=14
These three even numbers are 14, 16 and 18

A number is composed of four 10, three 1, three 0.01 and four 0.001, which is ()

A number consists of four 10, three 1, three 0.01 and four 0.001, which is (43.034)

On the map with a scale of 1 / 6000000, the distance between a and B is 10 cm. A and B drive from a and B at the same time and meet in 6 hours
How many kilometers per hour does car B travel?
Distance on the map: 5cm actual distance: 900km scale: ()
Distance on the map: 6.4cm actual distance: () scale: 1:50000
Distance on the map: () actual distance: 360km scale: 1:4000000

On a map with a scale of 1 / 6000000, the distance between a and B is 10 cm. When a and B depart from a and B at the same time, they meet after 6 hours. How many kilometers does a travel per hour and B travel per hour? B speed = 6000000 × 10 ﹣ 100 ﹣ 1000 ﹣ 6-55 = 100-55 = 45 km / h

The gate of a factory is shown in Figure 1, in which the quadrilateral ABCD is a square, the upper part is a semicircle with ab as the diameter, where ad = AB = 2m, and there is one full of goods
The truck is 2.5 meters high and 1.6 meters wide. Can the truck pass through the factory gate? Explain the reason

1.6 △ 2 = 0.8m
2 △ 2 = 1m
√ (1 & # 178; - 0.8 & # 178;) = 0.6m
2 + 0.6 = 2.6m ＞ 2.5m
So I can pass

There are 240 tons of coal in pile a, B and C. the weight ratio of pile a to pile B is 4:3, and pile C is 10 tons more than pile B. how many tons of coal are there in pile a, B and C?

Let a 4x, B 3x, then C 3x + 10
4x+3x+(3x+10)=240
10x=230
x=23
So a 92 tons, B 69 tons, C 79 tons

Mean inequality: how to prove that HN ≤ GN, HN is harmonic mean and GN is geometric mean
I can prove that QN ≥ an ≥ GN. I can't think of the last GN ≥ HN

.
It is proved that an ≥ GN, HN ≤ GN is exactly the same as him
For the denominator of harmonic mean, the algebraic geometric mean inequality is used, and each reciprocal is regarded as a term
This simple, more difficult point is the proof of algebraic set average
Application of Algebraic Geometric mean to reciprocal sum of harmonic mean

After nine hours of traveling from a to B, the two cars meet each other. Car a runs 20 kilometers less than car B per hour. The speed ratio of car B is 7 to 9. How many kilometers are there between a and B?

Party A and Party B per hour
20 △ 9-7 x (9 + 7) = 20 △ 2x16 = 160 km
apart
160x9 = 1440 km

If the solution set of X-1 ＞ A and X + 1 ＜ 5 is 1 ＜ x ＜ 3, then a =, B =

x-1＞a,x+1＜b
x>a+1, x