Simple calculation problem （1）(1+3+5+… +1999+2000+2001）-（2+4+6+… +1998+2002） （2）99… 9 [2000 9] * 99 9 [2000 9] + 199 9 [2000 9s]

Simple calculation problem （1）(1+3+5+… +1999+2000+2001）-（2+4+6+… +1998+2002） （2）99… 9 [2000 9] * 99 9 [2000 9] + 199 9 [2000 9s]

First, is 2000 behind,
Subtract - 1 for each item, total - 1001
The second: the original formula = (10 ~ 2000-1) ~ 2 + 19999 (2000 9)
=10 ~ 4000 is 4000 power of 10

Super simple calculation problem
3 and 2 / 1 times minus 7 / 5 minus 7 / 5 times 2 and 1 / 2 minus 1 / 2 divided by 7 / 5

1. Original formula = (7 / 3 * - 5 / 7) - (- 5 / 7 * 5 / 2) - (- 1 / 2) / 7 / 5))
=-3/5+25/14+5/14
=-3/5+30/14
=108/70
=54/35
2. Original formula = 7 / 3 * (- 5 / 7 - (- 5 / 7 * 5 / 2) - (- 1 / 2) / 7 / 5))
=7/3*(-5/7+25/14+5/14)
=7/3*20/14
=10/3

Using factorization calculation: 1000 to the second power / 252 to the second power - 248 to the second power =?

It's easy to break 248 into 250-2! You try!

How to distinguish permutation and combination in mathematical probability
It's the arrangement for what situation and the combination for what situation

As long as there is a design to the order of the problem, it is necessary to use the permutation
For example:
How many ways can three students divide three different books?
There are 6 kinds of A3, 3 = 6
2. How many ways to put six different books on the same shelf?
It can be understood that after arranging all six books, they will be moved to the bookshelf
So there are a 6,6 = 120 species
As for the combination, he has nothing to do with the order. He just takes out what he wants and puts it together
For example, three of the six books are:
C6,3=20
At last, it is summarized as follows
In fact, the arrangement is based on the combination, take out the things, and then take a shot, it becomes the arrangement
This can be explained from the formula
Am,n = Cm,n * An,n
It means that n permutations are selected from m, n combinations are selected from m, and then n permutations are completed by themselves
So it's easy to understand. Just remember that permutations are combinations

A simple method is used to calculate: 54 × 27 + 52 × 27-6 × 27

Extraction method: 27x (54 + 52-6)

Finding the maximum value of - 3x ^ 2 + 4x + 2 by formula method
Such as the title

-3x^2+4x+2
=-3(x^2-4/3 x- 2/3)
=-3(x^2-4/3 x+ 4/9 -10/9)
=-3(x-2/3)^2+10/3
-3(x-2/3)^2≤0
The maximum value is 10 / 3

What's 13 and 3 in 8 minus 18 and 2 in 8

13 and 3 in 8 minus 18 and 2 in 8
=13-18+3/8-2/8
=-5+1/8
=-4 and 7 / 8

How to solve 28-4x = 3x-7

28-4X=3X-7
4x+3x=28+7
7x=35
x=5

(5 / 24 + 3 / 18) * 24 * 18

=5/24*24*18+3/18*18*24
=90+72
=162

Explanation of quadratic function
Given that the image of quadratic function y = AX2 + BX + C is shown in the figure, the following judgment is incorrect
A abc>0 B b2-4ac>0
C 2a+b>0 D 4a-2b+c

First of all, a > 0 is obtained from the opening direction. Because the y-axis intersects the negative half axis to get C0 (4ac - B ^ 2) / 4A 0, so 4A > 0, because: (4ac - B ^ 2) / 4A 0
So C is right
D. Taking x = - 2, we can find from the trend of the image that the ordinate of the corresponding point is on the positive half axis of the Y axis, so 4a-2b + C