Calculate the value of (1999 ^ 3-1000 ^ 3-999 ^ 3) / (1999 × 1000 × 999)

Calculate the value of (1999 ^ 3-1000 ^ 3-999 ^ 3) / (1999 × 1000 × 999)

（1999^3-1000^3-999^3）=1000^3+3*1000^2*999+3*1000*999^2+999^3-1000^3-999^3=3*1000^2*999+3*1000*999^2
（1999^3-1000^3-999^3)/（1999×1000×999）
=(3*1000^2*999+3*1000*999^2)/（1999×1000×999）
=(3*1000+3*999)/1999=3*(1000+999)/1999
=3

Calculation (1999 ^ 3-1000 ^ 3-999 ^ 3) / (1999 * 1000 * 999)

There is a formula: x ^ 3 + y ^ 3 + Z ^ 3-3xyz = (x + y + Z) (x ^ 2 + y ^ 2 + Z ^ 2-xy-yz-xz) let x = 1999, y = - 1000, z = - 999 to get 1999 ^ 3-1000 ^ 3-999 ^ 3-3 * 1999 * (- 1000) * (- 999) = (1999-1000-999) (x ^ 2 + y ^ 2 + Z ^ 2-xy-yz-xz) = 0, so 1999 ^ 3-1000 ^ 3-999 ^ 3 = 3 *

Calculation: 1000 + 999-998 + 997 + 996-995 + +103+102-101=______ ．

1000+999-998+997+996-995+… +103+102-101，=1001+998+995+… +So the answer is: 165750

（9999+9997+.+9001）-（1+3+.+999）

（9999+9997+.+9001）-（1+3+.+999）
=(9999-999)+(9997-997)+(9995-995)+.+(9001-1)
=9000+9000+.+9000
Number of items = (999-1) △ 2 + 1 = 500
therefore
Original formula = 9000 × 500
=450000

9 + 99 + 999 =? How to calculate?

（10－1）＋（100－1）＋（1000－1）＝1110－3＝1107

Is there any clever way to calculate 999 * 99 * 9

﹙1000－1﹚×﹙100－1﹚×﹙10－1﹚＝ 890 109

A = 1 / (2007 * 998), B = / (2006 * 999), comparing the size of a and B? A, a is greater than B; B, a is less than B; C, a is equal to B; D, not sure

A = 1 / (2007 * 998), B = / (2006 * 999), compare the size of a and B? First look at the denominator 2007 * 998 = 2006 * 998 + 1 * 998 x2006 * 999 = 2006 * 998 + 2006 * 1 y, that is: compare X and y, y is obviously larger than x, but this is a score, so the result is opposite, so a and a are greater than B“

Compare the size of - 98 / 99 and - 998 / 999
Use it quickly

-98/99+(-1/99)=-1
-998/999+(-1/99)-998/999

999 x 998998999 - 998 x 999999998
X = multiply sign
It's the whole process····
It's a simple calculation

=999 x (998998998+1) - 998 x (999999999 -1)
=（999 x 998 x 1001001 +999）-（998 x 999 x1001001 -998)
=998 + 999
=1997

999 * 998998999-998 * 9999999998 =? Indicate the solution

=999 x (998998998+1) - 998 x (999999999 -1)
=（999 x 998 x 1001001 +999）-（998 x 999 x1001001 -998)
=998 + 999
=1997