Calculation: (1 / 2 + 1 / 3 +... 1 / 2006) (1 + 1 / 2 + 1 / 3 +... 1 / 2005) - (1 + 1 / 2 +... 1 / 2006) (1 / 2 + 1 / 3 +... 1 / 2005) Write out the calculation process

Calculation: (1 / 2 + 1 / 3 +... 1 / 2006) (1 + 1 / 2 + 1 / 3 +... 1 / 2005) - (1 + 1 / 2 +... 1 / 2006) (1 / 2 + 1 / 3 +... 1 / 2005) Write out the calculation process

simple form
=(1/2+1/3+...1/2006)*1+(1/2+1/3+...1/2006)(1/2+1/3+...1/2005)-(1/2+1/3+...1/2005)-(1/2+...1/2006)(1/2+1/3+...1/2005)
=1/2006

8 + 8.8 + 88.8 + 888.8 + 8888.8 + 88888.8 + 888888888.8,

0.8+8.8+88.8+888.8+8888.8+88888.8+888888.8=0.8x7+8x6+80x5+800x4+8000x3+80000x2+800000x1=5.6+48+400+3200+24000+160000+800000=760000+24000+3200+400+48+5.6=784000+3200+400+48+5.6=787200+448+5.6=787648+5....

88888 = 2 888888888 = 2 8888888 = 2 88888888 = 2 888888888888 = 2 make the equation hold

(8+8)×8÷8÷8 =2
(8+8+8+8)÷(8+8)=2
(8+8)×8×8÷8÷8÷8=2
(8+8+8+8)÷(8+8)×8÷8=2
(8+8+8+8+8+8)÷(8+8+8)=2

5 + 55 + 555 + 5555 + ······ + 55 ······ 55 {2010 five} sum

Sn=5+55+555+…… +55…… 55 (N 5)
=5*[1+11+111+…… +11…… [11 (n 1)]
=5/9*[9+99+999+…… +99…… 99 (n 9)]
=5/9(10-1+100-1+1000-1+…… +10^n-1)
=5/9[10*(1-10^n)/(1-10)-n]
=5/81*[10^(n+1)-9n-10]
S2010=5/81*(10^2011-18100)

The sum of divisor, quotient and remainder is 223. How much is the divisor?

That is to say, the sum of divisors is 223-7-5 = 211
(a-7)/b=5
a+b=211
The divisor a = 177

After 3 4 7 11... Every number is the sum of the first two numbers, then what is the remainder of the number 2007 divided by four

The remainder of this column divided by 4 is:
3,0,3,3,2,1,3,0,3,3,2,1,3,0.
3,0,3,3,2,1, cycles, 6 in each group
2007÷6=334...3
The third one in group 335 is 2007, which is 3
So the remainder is 3

When one natural number is used to remove another, the incomplete quotient is 8 and the remainder is 16. The sum of the divisor, divisor, quotient and remainder is 463. What is the divisor?

Divisor = divisor × quotient + remainder = 8 divisor + 16
Divisor + divisor + quotient + remainder = 463
8 divisor + 16 + divisor + 8 + 16 = 463
9 divisor = 463-16-8-16 = 423
Divisor = 423 △ 9 = 47
Comprehensive formula: (463-16-8-16) / (8 + 1) = 423 △ 9 = 47

The quotient is 8 and the remainder is 16. The sum of the divisor, divisor, quotient and remainder is 463
I'm going to use division with remainder,

Divisor (463-8-16-16) / (8 + 1) = 423 / 9 = 47

The quotient of dividing two natural numbers is 8 to 6, and the sum of divisor, divisor, quotient and remainder is 463
What are the divisor and divisor?

Divisor = quotient x divisor + remainder

Use a natural number to remove another natural number. The incomplete quotient is 13 and the remainder is 22. The sum of divisor, divisor, quotient and remainder is 463. What is the divisor?

463-22=441
13x+x+13=447
14x=434
x=31
13x=403
Divisor = 403