= -101/100

\(B=-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{98.99}-\frac{1}{99.100}\\ =-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\\ =-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\\ =-\left(1-\frac{1}{100}\right)=\frac{-99}{100}\)

<br class="Apple-interchange-newline"><div></div>B=−11.2 −12.3 −13.4 −...−198.99 −199.100  \\ =−(11.2 +12.3 +13.4 +...+198.99 +199.100 ) \\ =−(1−12 +12 −13 +13 −14 +...+198 −199 +199 −1100 ) \\ =−(1−1100 )=−99100 

A=1.2+2.3+3.4+........+98.99 
3A=1.2.3+2.3.3+3.4.3+........+98.99.3 
3A=1.2.3+2.3.(4 -1) +3.4.(5 -2)+........+98.99.(100 -97) 
3A=1.2.3+2.3.4 -1.2.3 +3.4.5 -2.3.4 +........+98.99.100 -97.98.99 
3A=98.99.100 
===>A=(98.99.100)/3

#Japhkiel#

A=1.2+2.3+3.4+........+98.99 
3A=1.2.3+2.3.3+3.4.3+........+98.99.3 
3A=1.2.3+2.3.(4 -1) +3.4.(5 -2)+........+98.99.(100 -97) 
3A=1.2.3+2.3.4 -1.2.3 +3.4.5 -2.3.4 +........+98.99.100 -97.98.99 
3A=98.99.100 
A=\(\frac{98.99.100}{3}=\frac{970200}{3}=323400\)

Đặt A\(=1\cdot2+2\cdot3+3\cdot4+......+98\cdot99\), ta có

\(3A=1\cdot2\cdot3+2\cdot3\cdot3+.....+98\cdot99\cdot3\)

\(=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+98\cdot99\cdot\left(100-97\right)\)

\(=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+....+98\cdot99\cdot100-97\cdot98\cdot99\)

\(=98\cdot99\cdot100\)

\(\Rightarrow A=\frac{98\cdot99\cdot100}{3}=323400\)

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

3S=1.2.3-0.1.2+2.3.4-1.2.3+...+99.100.101-98.99.100

3S=(1.2.3+2.3.4+...+99.100.101)-(0.1.2+1.2.3+...+98.99.100)

3S=99.100.101-0.1.2

3S=99.100.101

S=\(\frac{99.100.101}{3}=333300\)

S = 1 . 2 + 2 . 3 + 3 . 4 + ...... + 99 . 100 

Gấp S lên 3 lần ,ta có: 

S . 3 = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + … + 99 . 100 . 3 

S . 3 = 1 . 2 . 3 + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) + … + 99 . 100 . ( 101 - 98 ) 

S . 3 = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + … + 99 . 100 . 101 - 98 . 99 . 100 

S . 3 = 99 . 100 . 101 

S = 99 . 100 .101 : 3 

S = 33 . 100 . 101 

S = 333300

Gọi A là biểu thức ta có: 
S = 1.2+2.3+3.4+......+98.99+99.100 
Gấp S lên 3 lần ta có: 
S . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
S . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
S . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
S . 3 = 99.100.101 
S = 99.100.101 : 3 
S = 33.100.101 
S = 333 300

Đặt :

\(A=\)\(1.2+2.3+3.4+.................+98.99\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...............+98.99.3\)

\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+.................+98.99.\left(100-97\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+................+98.99.100-97.98.99\)\(\Rightarrow A=\dfrac{98.99.100}{3}=323400\)

Đặt A=1.2+ 2.3+ 3.4+ ...+ 98.99

3A=1.2.3+ 2.3.3+ 3.4.3+ ...+ 98.99.3

3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+98.99.(100-97)

3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99

3A=98.99.100

A=98.99.100\(\div\)3

A=323400

B = 1.2 + 3.4 + 5.6 +...+ 98.99

3B = 1.2(3-0) + 2.3(4-1) ...... 98.99 (100-97)

3B = 1.2.3-0.2.3.4-1 ......... 98.99.100-97

3B = ( 1.2.3+2.3.4+.....+98.99.100) - ( 0.1.2+ 1.2.3+.... + 97.98.99)

3B = 98.99.100

3B = 970200

  B = 323400

C=1*2+2*3+3*4+...+98*99

C=2+6+12+...+9702

C=2+9702

C=9704

vay C=9704

D=(1*99+2*99+3*99+...+99*99)-(1*2+2*3+3*4+...+98*99)

D=(99+198+297+...+9801)-(2+6+12+...+9702)

D=(99+9801)-(2+9702)

D=9900-9704

D=196

vay D=196

ai di qua dong tinh thi nho h cho minh nhe

\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{98.99}+\frac{9}{99.100}\)

\(A=\frac{1}{9}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(A=\frac{1}{9}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=\frac{1}{9}.\left(1-\frac{1}{100}\right)\)

\(A=\frac{1}{9}.\frac{99}{100}\)

\(A=\frac{11}{100}\)

A = 9/1.2 + 9/2.3 + 9/3.4 +...+ 9/98.99 + 9/99.100

   = 9. (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/98 - 1/99 + 1/99 - 1/100)

   = 9. (1 - 1/100)

   = 9 . 99/100

   = 891/100

bạn hỏi gì vậy ?

dấu chấm là phép nhân ai bt làm giải giúp mik nha mik tích cho

Đặt \(A=1.2+2.3+...+98.99\)

\(\Rightarrow3A=1.2.3+2.3.3+....+98.99.3\)

\(=1.2.3+2.3.\left(4-1\right)+...+98.99.\left(100-97\right)\)

\(=1.2.3+2.3.4-1.2.3+...+98.99.100-97.98.99\)

\(=98.99.100\)

\(=970200\)

\(\Rightarrow A=970200:3=323400\)