We have : 37 = 3 + 5 + 29 (c1)

                 37 = 3 + 11 + 23 (c2)

                 37 = 5 + 13 + 19 (c3)

Drees is three ways are there to write 37 

We have : 100 + 500 : 5 - 40 

= 100 + 100 - 40

= 200 - 40

= 160 

We have: abcdeg = abc000 + deg
= Abc. 100000 + deg
= Abc. 99999 + (abc + deg)
Which - 99999 is divisible by 37 so abc. 99999 is divisible by 37
- abc + deg is divisible by 37
So the distribution is divided by 37 (ddcm)

We have : \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right).......\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}......\dfrac{99}{100}\)

\(=\dfrac{1}{100}\)

You have : 300 = 2².3.5²

The number of integer factors 300 have is :

                      2.[(2 + 1)(1 + 1)(2 + 1)] = 36

                               Answer : 36. good

The area around the cube is:
                       A x a x 4 = a x a x 4
Total cube area is:
                       A x a x 6 = a x a x 6
The head for the total area larger than the surrounding area is: a x a x 6 - a x a x 4 = 162
The total area larger than the surrounding area is:
A x a x (6 - 4) = a x a x 2
A x a is:
              162: 2 = 81 (cm2)
Because 81 = 9 x 9, the edge of the cube is 9 cm
Cubic volume is:
              9 x 9 x 9 = 729 (cm3)
                        Answer: 729 cm3

Good . You Good 

We have 

Apply (1) to the expression, we have : 1³ + 2³ + 3³ + ... + 2008³ 

= (1 - 1)1(1 + 1) + 1 + (2 - 2)2(2 + 2) + 2 + ....... + (2008 - 2008) 2008 (2008 - 2008) + 2008

= 1 + 2 + 1.2.3 + 3 + 2.3.4 + ........ + 2008 + 2007.2008.2009

= (1 + 2 + 3 + ...... + 2008) + (1.2.3 + 2.3.4 + ...... + 2007.2008.2009)

= 2017036 + 2007.2008.2009.2010 / 4 

= The number to mik not count 

You have : 300 = 220,30,52

The number of integer factors 300 have is :

                      2.[(2 + 1)(1 + 1)(2 + 1)] = 36

                               Answer : 36. good

We have : ƯCLN(140;240) = 20

Dress the largest square can be 20 cm x 20 cm

I have : abcabc = abc x 1001

                         = abc x 91 x 11

Ghost abc \(\in\) N Candle abcabc divisible by 11 

Good

n(n + 2) = (n + 1)² - 1 

We have : ab = 8(a + b) 

=> 10a + b = 8a + 8b

=> 10a - 8a = 8b - b

=> 2a = 7b

=> a = 7 ; b = 2

So ab is 72

BCNN (a,b) = 50 => a,b = 25;50 . 10;50 . 1;50 . 2;50 . 5;50 

Good  

Volume Min block is : 

              11.3.2 = 66 (in³)

                  Answer : 66 in³

Replacing x = 1/2 we have: 4x - 3a = 0  

<=> 4.1/2 - 3a = 0

=> 2 - 3a = 0

=> 3a = 2

=> a = 2/3

Dress a = 2/3 good

For : \(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\)

\(\Rightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{4}+.....+\dfrac{1}{128}\)

\(\Rightarrow2A-A=1-\dfrac{1}{128}\)

\(\Rightarrow A=\dfrac{127}{128}\)

Ta có : 3 + 3² + 3³ + ...... + 3²⁰⁰⁰

=> 3A = 3² + 3³ + 3⁴ + ...... + 3²⁰⁰¹

=> 3A - A = 3²⁰⁰¹ - 3

=> 2A = 3²⁰⁰¹ - 3

=> A = \(\dfrac{3^{2001}-3}{2}\)

Good

Hao made the number is:

  236 x 1/3 = ?

No

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.......+\dfrac{1}{999999.1000}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.......+\dfrac{1}{999}-\dfrac{1}{1000}\)

\(=1-\dfrac{1}{1000}\)

\(=\dfrac{999}{1000}\)

a, x ³ .x ⁴ = x⁷

b, 1⁵.1⁴=1