=1999/1000

Mik chắc chắn vì mik thi Violympic r

ra 1999/1000 nha bạn

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.........+\frac{1}{999x1000}+1\)

= \(1-\frac{1}{1000}+1\)

= \(\frac{999}{1000}+1\)

= \(\frac{1999}{1000}\)

P=1x2+2x3+3x4+...+2017x2018

3P = 1x2x3 + 2x3x3 + 3x4x3 + ... + 2017x2018x3

3P = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... +2017x2018x(2019-2016)

3P = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 2017x2018x2019 - 2016x2017x2018

3P = 2017x2018x2019

P = 2017x2018x2019 : 3

P = 2739315938 

P = 1x2+2x3+3x4+...+2017x2018

3xP = 1x2x3+2x3x3+3x4x3+...+2017x2018x3

3xP = 1x2x3+2x3x(4-1)+3x4x(5-2)+...+2017x2018x(2019-2016)

3xP = 1x2x3+2x3x4-2x3x1+3x4x5-3x4x2+...+2017x2018x2019-2017x2018x2016

3xP = 2017x2018x2019

3xP = 8217947814

P = 8217947814 : 3

P = 2739315938 

A = 2  +  ( 2+ 1).4  +  ( 4 + 1)6  + … +  (98 + 1).100

    = 2  +  2.4 + 4  +  4.6 + 6 + … +  98.100  +  100

    = (2.4 +  4.6 + … +  98.100 )  +  (2  +  4  +  6 + … +  100)

    = 98.100.102 : 6 + 102.50:2

    = 166600 + 2550

    = 169150

= 333300

=333300

k mình nha tran huyen trang 

B x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

= 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

= 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

= 99x100x101

B = 99x100x101 : 3

= 333300

nhanh k minh

B= 1x2+3x4+5x6+...+99x100

=> Bx3= 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ...+ 99x100x3

=> Bx3= 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3)+...+99x100x(101-98)

=> Bx3= 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 +4x5x6 - 3x4x5 +...+ 99x100x101 - 98x99x100

=> Bx3= 99x100x101

=> B= 99x100x101:3

=> B= 333300

1 x 2 = 2 

5 x 6 = 30 

2 x 3 = 6 

6 x 7 = 42 

3 x 4 = 12 

7 x 8 = 56 

4 x 5 = 20 

8 x 9 = 72 

HT

TL

1x2=2           2x3=6               3x4=12                     4x5=20

5x6=30             6x7=42                    7x8=56                      8x9=72

nha

HT

2                     6                         12                                20

30                    42                        56                                72 

k mình nha !!

gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

**** nha ^^

Gọi biểu thức trên là A, ta có :

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

A = 1x2 + 2x3 + 3x4 + ... + 98x99 + 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x4 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3 x ( 4 - 1 ) + 3x4( 5 - 2 ) + 4x5x (6 - 3 ) + .... + 99x100( 101 - 98 )

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100

A x 3 = 99 x 100 x 101

A = 99x 100 x 101 : 3 

A = 333300

\(S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2010.2011}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(S=1-\frac{1}{2011}\)

\(S=\frac{2010}{2011}\)

Phân tích: 1 / 1 x 2 = 1 - 1/2

1/2.3 = 1/2 - 1/3

. ....Bạn làm tương tự các số còn lại...

Ta được: 1 - 1/2 + 1/2 - 1/3 + ....+1/ 2010 - 1/2011

= 1 - 1/2011

= 2010/2011