tham the 

có giỏi thì làm một câu xem nào

đơn giản à

\(A=1.2+2.3+3.4+...+99.100\)

\(\Rightarrow3A=1.2.3+2.3\left(4-1\right)+3.4\left(5-2\right)+...+90.100\left(101-98\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(\Rightarrow3A=99.100.101\)

\(\Rightarrow A=\left(99.100.101\right):3\)

\(\Rightarrow A=333300\)

\(B=1.3+2.4+3.5+...+99.101\)

\(\Rightarrow B=1\left(2+1\right)+2\left(3+1\right)+3\left(4+1\right)+...+99\left(100+1\right)\)

\(\Rightarrow B=1.2+1+2.3+2+3.4+3+...+99.100+99\)

\(\Rightarrow B=\left(1.2+2.3+3.4+...+99.100\right)+\left(1+2+3+...+99\right)\)

\(\Rightarrow B=333300+4950\)

\(\Rightarrow B=338250\)

\(D=1.2.3+2.3.4+3.4.5+...+98.99.100\)

\(\Rightarrow4D=1.2.3.4+2.3.4.4+...+98.99.100.4\)

\(\Rightarrow4D=1.2.3\left(4-0\right)+2.3.4\left(5-1\right)+...+98.99.100\left(101-97\right)\)

\(\Rightarrow4D=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+98.99.100-97.98.99\)

\(\Rightarrow4D=98.99.100\)

\(\Rightarrow D=\left(98.99.100\right):4=242550\)

kết bạn kiểu gì

a)1+3+5+7+9+...+x=1600

=>[(x-1):2+1].(x+1)/2=1600

=>(1/2.x-1/2+1).(x+1)=1600:1/2

=>(1/2.x-1/2+1).(x+1)=3200

=>(x+1)².1/2=3200

=>(x+1)²       =3200:1/2

=>(x+1)²=6400

=>x+1=80

=>x=80-1=79

a ) 1 + 3 + 5 + ... + x = 1600

Theo bài ra ta có :

[ ( x -1 ) : 2 + 1 ]² = 1600

  ( x - 1 ) : 2 + 1    = 40 ( căn bậc 2 của 1600 )

  ( x - 1 ) : 2          = 40 - 1

  ( x - 1 ) : 2          = 39

     x - 1                = 39 . 2

     x - 1                = 78

          x                = 78 + 1

          x                = 79

Vậy x = 79

b ) A = 1.2 + 2.3 + 4.3 + ..... + 99.100

A x 3 = 1.2.3 + 2.3.3 + 4.3.3 + ..... + 99.100.3

A x 3 = 1.2.( 3 - 0 ) + 2.3.( 4 - 1 ) + 4.3.(  5 - 2 ) + ... + 99.100.( 101 - 98 )

A x 3 = 1.2.3 - 1.2.0 + 2.3.4 - 1.2.3 + 4.3.5 - 4.3.2 + ..... + 99.100.101 - 99.100.98

A x 3 = 99.100.101

A       = 99.100.101 : 3

A       = 333300

Vậy A = 333300

c ) 

     B = 1.3 + 2.4 + 3.5 + ..... + 99.101

B x 3 = 1.2.3 + 2.4.2 + 5.3.2 + ..... + 99.101.2

B x 3 = 1.3.( 2 - 0 ) + 2.4.( 3 - 1 ) + 5.3.( 4 - 2 ) + ... + 99.101.( 102 - 100 )

B x 3 = 1.2.3 - 1.3.0 + 2.3.4 - 1.2.3 + 4.3.5 - 5.3.2 + ..... + 99.101.102 - 99.101.100

B x 3 = 99.101.102

B       = 99.101.102 : 3

B       = 339966

Vậy B = 339966

d ) C=1.4+2.5+3.6+...+99.102

    C = 1.(2+2) + 2.(3+2) + 3.(4+2)+...+99.(100+2) 

    C = 1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2 

    C = (1.2+2.3+3.4+...+99.100)+2(1+2+3+...+99) 

    C = 333300 + 9900 

    C = 343200

Vậy C = 343200

e ) D = 1.2.3 + 2.3.4 + 3.4.5 + .... + 98.99.100

=> 4D = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 98.99.100.4

=> 4D = 1.2.3.4 + 2.3.4.( 5 - 1 ) + 3.4.5.( 6 - 2 ) + .... + 98.99.100.( 101 - 97 )

=> 4D = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + .... + 98.99.100.101 - 97.98.99.100

=> 4D = ( 1.2.3.4 - 1.2.3.4 ) + ( 2.3.4.5 - 2.3.4.5 ) + ...... + ( 97.98.99.100 - 97.98.99.100 ) + 98.99.100.101

=> 4D = 98.99.100.101

=> S = 98.99.100.10 : 14 

=> S = 24497550

nhiều quá vậy ?

Gọi A là biểu thức ta có: 
CÂU1 :A = 1.2+2.3+3.4+......+99.100 
          3A = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
          3A = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
          3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
          3A = 99.100.101 
          A = 99.100.101 : 3 
          A = 33.100.101 
          A = 333 300

cau B

B=1.3+2.4+3.5+......+99.101

B=1.(2+1)+2.(3+1)+3.(4+1)+.......+99.(100+1)

B=1.2+1+2.3+2+3.4+3+.......+99.100+99

B=1.2+2.3+3.4+........+99.100+(1+2+3+....+99)

B=99.100.101+(1+\(\frac{\left(2+99\right).98}{2}\))

B=.......