Prove cN0 + +Cnn=2^n combination How to prove it?

Prove cN0 + +Cnn=2^n combination How to prove it?

2^n=(1+1)^n
=Cn0*1^n+Cn1*1^(n-1)*1+…… +Cnn*1^n
=Cn0+Cn1+…… +Cnn

1-1/2cn1+1/3cn2-1/4cn3.+(-1)^n 1/(n+1)cnn

1/(i+1)cni=1/(n+1)c(n+1)i+1
The original formula = - 1 / (n + 1)

A class of a students participate in tree planting activities, including B boys (b < a), if only completed by boys, each need to plant 15 trees; if only completed by girls, each need to plant trees______ A tree

The total number of trees planted is 15b, and the number of girls is A-B, so each girl needs to plant 15ba − B trees

Handsome guy, find the maximum and minimum value of y = | X-1 | - | x + 5 |. We're talking about the simplification of absolute value

x> 1, y = X-1 - (x + 5) = - 6
-5 ≤ x ≤ 1, y = - (x-1) - (x + 5) = - 2X-4, when x = - 5, take the maximum value of 6, when x = 1, take the minimum value of - 6
When x

There are 54 students in a class. Can there be 2 students who celebrate their birthday in the same week? Why?

Suppose proposition a: there are no two birthdays in a week. If proposition a is satisfied, there are at least 54 weeks in a year, but there are only 52 weeks in a year, so proposition a does not hold. Therefore, there must be two or more birthdays in the same week among the 54 students

The square of 4A minus 4A plus 1
Factorization

4a2-4a+1
=(2a-1)2
This is the subtraction formula in the complete square formula

The distance between the car and the truck is 165 meters. The car travels 80 kilometers per hour and the truck 65 kilometers per hour. When will the car catch up with the truck in front?

165÷（80-65）＝165÷15＝11h
A: 11 hours to catch up

① Given the equation of AB: the square of X + 2x-5 = two real roots of 0, find the square of a + AB + 2A
② The equation about X is known
The square of kx-2 (K + 1) x + k-1 = 0 has two unequal real roots. ① find the value range of K; ② whether it is in the real number k, make the two real roots, reciprocal sum of the equation equal to 0
③ Question: if the sum of the reciprocal of two real roots of equation M's Square X's Square - (2m + 3) x + 0 is n, find the value range of n
④ Question: let a, B, C be the square of (a + B + C) + the square of (a-b-c) + the square of (b-c-a) + the square of (c-b-a)

1. A ^ 2 + 2A - 5 = 0, Veda theorem AB = - 5
So the square of a + AB + 2A = 5 + 2 × (- 5) = - 5
2.,①
K is not equal to 0
The discriminant 4 (K + 1) ^ 2 - 4K (k-1) > = 0, that is, k > = - 1 / 3 and K is not equal to 0
②
1 / X1 + 1 / x2 = (x1 + x2) / x2x1 = 2 (K + 1) / K divided by (k-1) / k = 2 (K + 1) / (k-1)
Let it be equal to 0, then k = - 1, k > = - 1 / 3 and K is not equal to 0
So there is no K
3. The condition is not complete, the equation is not complete
4. The sum of two sides is greater than the third side, and the difference is less than the third side
Original formula = (a + B + C) + (B + C-A) + (a + C-B) + (B + A-C)
= 2a + 2b + 2c

A and B start from a and B at the same time and travel in opposite directions. A travels 50 kilometers per hour and B 40 kilometers per hour. A reaches the midpoint one hour earlier than B. how many hours does a reach the midpoint?

40 × 1 ^ (50-40), = 40 ^ 10, = 4 (hours); answer: a reaches the midpoint in 4 hours

The solution of the equation 0.5x-2 = 0.8 (2x-3.5) is that 2 has a farm, the sum of the number of hens and the number of pigs is 70, and the sum of the number of legs is 196, then the number of hens is more than the number of pigs. 3 if the solution of the equation 3x + (2a + 1) = x - (3a + 2) is 0, then a is equal to 4. According to the rules of football game planning, 3 points will be obtained if one game wins, 0 points will be obtained if one game draws, and 25 points will be obtained if one team loses 4 games in 15 games, How many games did the team win? 5 is a two digit number. The sum of the ten digit number and each digit is 7. If the two digit number is transposed, the two digit number is 45 larger than the original number, then the original two digit number is 7

1.0.5x-2 = 0.8 (2x-3.5) 0.5x-2 = 1.6x-2.81.6x-0.5x = 2.8-21.1x = 0.8x = 8 / 11 2. There is a farm where the sum of the number of hens and pigs is 70, and the sum of the number of legs is 196, then the number of hens is more than that of pigs