A=2(\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\))=2(\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\))

=> A=2(\(\frac{1}{1}-\frac{1}{100}\))=2.\(\frac{99}{100}=\frac{99}{50}\)

ĐS: A=99/50

\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+\frac{2}{4\times5}+...+\frac{2}{99\times100}\)

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{99\times100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{1}-\frac{1}{100}\)

\(=\frac{99}{100}\)

\(2\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=2\times\left(1-\frac{1}{100}\right)\)

\(=2\times\frac{99}{100}\)

\(=\frac{99}{50}\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{99.100}\)

= \(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\right)\)

= \(2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\right)\)

= \(2.\left(1-\frac{1}{100}\right)\)

= \(2.\frac{99}{100}\)

= \(\frac{99}{50}\)

gấp lắm ạ giúp em với

\(\Leftrightarrow y\cdot\dfrac{99}{50}=\dfrac{198}{100}=\dfrac{99}{50}\)

hay y=1

Ta có : P = 1.2.2 + 2.3.3 + ....+ 99.100.100

=1.2.(3 - 1) + 2.3.(4 - 1) + ....+99.100.(101 - 1)

= (1.2.3 + 2.3.4 + .... + 99.100.101) - (2.3 + 3.4+.....+99.100)

Đặt B = 1.2.3 + 2.3.4 + 4.5.6 +...+ 99.100.101

4B = 1.2.3.(4 - 0)+2.3.4.(5 - 1) + ... + (99.100.101(102 - 98)

4B = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 +...+ 99.100.101.102 - 98.99.100.101

4B = 99.100.101.102

4B = 101989800

B = 25497450

Đặt C = 1.2 + 2.3 + 3.4 +...+ 99.100

3C = 1.2.(3 - 0) + 2.3.(4 - 1) +...+ 99.100.(101 - 98)

3C = 1.2.3 + 2.3.4 - 1.2.3 +...+ 99.100.101 - 98.99.100

3C = 99.100.101

3C = 999900

C = 999900 : 3

C = 333300

Vậy: P = 25497450 – 333300 = 25164150 

Giải cụ thể mk k cho

Đặt \(A=\frac{2}{1.2}+\frac{2}{2.3}+...+\frac{2}{99.100}\)

\(A=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(A=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=2.\left(1-\frac{1}{100}\right)\)

\(A=\frac{2.99}{100}\)

\(A=\frac{99}{50}=1\frac{49}{50}\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{99.100}\)

\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=2\left(1-\frac{1}{100}\right)=2.\frac{99}{100}\)

\(=\frac{99}{50}\)

1x 2 + 2 x 3 + 3 x 4 + ...+ 99 x 100

Ta có: 

1 x 2 x 3                                           = 1 x 2 x 3

2 x 3 x 3     = 2 x 3 x ( 4 - 1)             = 2 x 3 x 4 -  1 x 2 x 3

3 x 4 x 3     =  3 x 4 x ( 5 - 2)            = 3 x 4 x 5 -   2 x 3 x 4 

........................................................= ........................................

99 x 100 x 3 = 99 x 100 x (101 - 98)  = 99 x 100 x 101 - 99 x 100 x 98

Cộng vế với vế ta có:

1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 +...+ 99 x 100 x 3 = 99 x100 x 101

(1 x 2 + 2 x 3 + 3 x 4 +...+ 99 x 100) x 3 =  99 x 100 x 101 

1 x 2 + 2 x 3 + 3 x 4 +...+ 99 x 100 = \(\dfrac{99\times100\times101}{3}\)

1 x 2 + 2 x 3 + 3 x 4 + ....+ 99 x 100 = 333300

333300

A = 1.2+2.3+3.4+......+99.100 
Gấp A lên 3 lần ta có: 
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
A . 3 = 99.100.101 
A = 99.100.101 : 3 
A = 33.100.101 
A = 333 300

bạn giải được không

3A=3.(1x2+2x3+3x4+....+99x100)

3A=3x1x2x+3x2x3+3x3x4+...+3x99x100

3A=(3-0)x1x2+(4-1)x2x3+(5-2)x3x4+...+(101-98)x99x100

3A=1x2x3-0+2x3x4-1x2x3+3x4x5-2x3x4+...+99x100x101-98x99x100

3A=99x100x101-0

3A=99x100x101

A=33x100x101

A=333 300

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 = 99x100x101 A = 333300