1 / X (x + 1) + 1 / (x + 1) (x + 2) + 1 / (x + 2) (x + 3) +... + 1 / (x + 2006) (x + 2007) process

1 / X (x + 1) + 1 / (x + 1) (x + 2) + 1 / (x + 2) (x + 3) +... + 1 / (x + 2006) (x + 2007) process

Solution: 1 / X (x + 1) + 1 / (x + 1) (x + 2) + 1 / (x + 2) (x + 3) +... + 1 / (x + 2006) (x + 2007)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……
+1/(x+2006)-1/(x+2007)
=1/x-1/(x+2007)
=[(x+2007)-x]/x(x+2007)
=2007/x(x+2007)
Note: just remember the formula 1 / X (x + 1) = 1 / X-1 / (x + 1)
In general: 1 / AB = (B-A) (1 / A-1 / b)

Given the square of X + the square of y-8x-10y + 41 = 0, find y / (the square of x-xy) + X / (the square of y-xy)

The square of X + the square of Y - 8x-10y + 41 = 0x & # 178; - 8x + 16 + Y & # 178; - 10Y + 25 = 0 (x-4) & # 178; + (Y-5) & # 178; = 0x-4 = 0y-5 = 0  x = 4Y = 5 find y / (the square XY of x) + X / (the square XY of Y) = Y / X (X-Y) - X / Y (X-Y) = (Y &  178; - X & # 178;) / XY (X-Y) = - (x + y) / xy = - (4 + 5) / 20 =

Taking x.x + y.y-8x-10y + 41 = 0, the value of X / {y.y-xy} + Y / {x.x-xy} is obtained
How to do it?

x²+y²-8x-10y+41=0
(x-4)²+(y-5)²=0
X-4 = 0 leads to x = 4, Y-5 = 0 leads to y = 5
x/(y²-xy)+y/(x²-xy)
=x/y(y-x)+y/x(x-y)
=x²/xy(y-x)-y²/xy(y-x)
=(x²-y²)/xy(y-x)
=-(x+y)(x-y)/xy(x-y)
=-(x+y)/(xy)
=-(4+5)/(4·5)
=-9/20

One pool has a storage capacity of 20 cubic meters, and a water pipe is used to inject water into the pool at the speed of 5 cubic meters per hour. At the same time, another drainage pipe is used to drain water out of the pool at the speed of 6 cubic meters per hour. (1) write the relationship between the storage capacity V (M3) of the pool and the inflow time t (hour) (pay attention to the value range of the independent variable); (2) when is the water in the pool drained?

(1) V = 20 + 5t-6t = 20-t (0 ≤ t ≤ 20); (2) get 0 = 20-t from the meaning of the question, and get t = 20

X Λ 2 / 3 and X Λ 1 / 2, which is a higher order infinitesimal
Why?

X ^ (2 / 3) is an infinitesimal of higher order
reason:
[x^(2/3)]÷[x^(1/2)]=x^(1/6)→0

7 and 2 / 3 plus 4 and 3 / 4 plus - 6 and 1 / 3 plus - 9 and 1 / 4

7 and 2 / 3 plus 4 and 3 / 4 plus - 6 and 1 / 3 plus - 9 and 1 / 4
=(7 2 / 3-6 1 / 3) - (9 1 / 4-4 3 / 4)
=1 and 1 / 3-4 and 1 / 2
=-3 and 1 / 6

Mathematics winter vacation homework of grade seven
1、 Fill in the blanks
1. It is known that a, B are opposite to each other, C, D are reciprocal to each other, and the absolute value of X is 3
（1）a+b=______ ；cd=______ ；x=______ ；
(2) Finding the value of 2005 power + 3cd-x & sup2; of (a + b)
2. If a and B are rational numbers and satisfy (a + b) & sup2; + | B-2 | = 0, then the power of a is B=______ .
3. The area of the Forbidden City in Beijing is 7.2x10 square meters, which is an approximate number____ It's a significant number, accurate to______ A bit
4. In 1999, a city completed the relocation of migrants in the Three Gorges Reservoir area to the fourth power of 1.05x10, which is the approximate number obtained by the rounding method, and the effective number is______ It's accurate to______ A bit
5. Column Algebra:
(1) The difference between the opposite number of the square of a and the square of the opposite number of a:______ .
(2) There is a two digit number, its ten digit number is a, and its one digit number is B. algebraic expression is used to express the sum of ten digit number and one digit number multiplied by the two digit number______ .
6.60°=______ Right angle=______ Flat angle=______ It's the corner
7.18°15′36〃=______ Calculation: 118 ° 18 '- 66 ° 23'=______ .
8. Only one pair of triangle plate can draw different angles greater than 0 ° and less than 180 °______ One
After 15 minutes, the clock turned______ Angle of
10. There is a mountain between a and B, and a railway passes through two points a and B. the direction of the railway measured in a is 63 ° 36 'by North by East, then it is 63 ° 36' by North by West in B______ Direction of construction, in order to make the railway accurately connected in the mountain
11. The degree of an angle is 70 ° 54 ′ 36 ", and its residual angle is______ Its complement is______ .
2、 Multiple choice questions
1. If a and B are rational numbers, a < 0, b > 0, and | a | > b |, then the size relation of a, B, - A, - B is ()
A.b＜-a＜-b＜a B.a＜-b＜b＜-a
C.b＜-a＜a＜-b D.-a＜-b＜b＜a
2. A store has two calculators with different prices, both of which sold for 80 yuan. One of them made a profit of 60% and the other lost 20%. In this transaction, the store ()
A. Don't lose don't earn B. earn 10 yuan C. lose 10 yuan D. earn 50 yuan
3. The direction of a looking at B is 30 ° north by East, then the direction of B looking at a is ()
A. South by East 60 ° B. south by West 60 ° C. south by east 30 ° D. south by West 30 ° C
4. If a car is driving on a straight road and is still going in the original direction after two turns, the angle of the two turns may be ()
A. Turn right 40 ° for the first time and turn left 140 ° for the second time
B. Turn left 40 ° for the first time and right 40 ° for the second time
C. Turn left 40 ° for the first time and turn right 140 ° for the second time
D. Turn right 40 ° for the first time and turn right 140 ° for the second time
5. If ∠ 1 and ∠ 2 are complementary angles, and ∠ 1 ＞ 2, then two times of the residual angle of ∠ 2 is equal to ()
A.∠1—∠2 B.∠1+∠2 C.∠1 D.∠2

1、 It is known that a and B are opposite to each other, C and D are reciprocal to each other, and the absolute value of X is 3. Find: (1) a + B = 0______ ；cd=1______ ；x=+3、-3______ (2) find the value of (a + b) ^ 2005 + 3cd-x ^ 2 = 0 ^ 2005 + 3 * 1-3 (or - 3) ^ 2 = 3-9 = - 62

If the resultant force of two common forces F1 and F2 is f, then ()
A. The resultant force F must be greater than any component B. the magnitude of resultant force F may be equal to F1 or equal to F2C. The resultant force F may be less than any component D. the magnitude of resultant force F increases with the increase of the angle between F1 and F2

A. The effect of a resultant force and several components is the same, but the magnitude of the resultant force is not necessarily greater than that of any component force, it can be less than or equal to the component force. So a is wrong and BC is correct; D. The magnitude of resultant force F decreases with the increase of the angle between F1 and F2, and the range of resultant force is between the difference and the sum of the two components

How much is three fourths less than its reciprocal

Because: (4 / 3) - (3 / 4) = (16 / 12) - (9 / 12) = 7 / 12,
So: 3 / 4 is 7 / 12 less than its reciprocal

What is the ancient and modern meaning of "Si Yuan bow and shoot"?

. think of the bow and shoot it
In this sentence, it means: where, where;
Where is there a bow and arrow tied with silk rope to shoot birds
Hand pull, quote, help