\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

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

     \(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.95}\)

   \(=\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{92-92}{92.95}\)

   \(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{92}-\frac{1}{95}\)

     \(=\frac{1}{2}-\frac{1}{95}=\frac{93}{190}\)

\(C=\frac{5}{6}+\frac{5}{66}+\frac{5}{176}+\frac{5}{336}\)

    \(=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}\)

    \(=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}\) 

    \(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}\)

     \(=1-\frac{1}{21}=\frac{20}{21}\)

[ HỌC TỐT]

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

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

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

\(A=\frac{100}{200}-\frac{2}{200}\)

\(A=\frac{98}{200}=\frac{49}{100}\)

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

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

\(A=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.95}\)

\(B=\frac{3}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{92}-\frac{1}{95}\right)\)

\(B=\frac{1}{2}-\frac{1}{95}=\frac{93}{190}\)

1 + 2 - 3 -4 + 5 + 6 -7 -8 + ... +97 +98 -99 -100 ( có: ( 100 - 1 ) : 1 + 1 = 100 )

= ( 1 +2 - 3 - 4 ) + ( 5 + 6 - 7 -8 ) + ... ( 97 + 98 - 99 +100 ) ( có 100 : 4 = 25 cặp )

 = - 4 + -4 + -4 + ... + -4 ( có 25 số hạng )

= ( -4 ) . 25

= -100

a, x + 1/9 - 3/5 = 3/6

    x + 1/9        = 3/6 - 3/5

    x + 1/9        = -1/10

    x                = -1/10 - 1/9

    x                = -19/90

19/90 nha

 720 : ( x . 2 + x . 3 ) = 3.2
720 : ( x . 2 + x.3 ) = 6
( x .2 + x.3 )           = 720 : 6 
x.2+x.3 = 120
x . ( 2 + 3 ) = 120
x . 5 = 120
     x     = 120 : 5 
    x      = 24

a: =(375-175)+(369-169)+...+(207-7)

=200+200+...+200

=200*[(375-207)/2+1]

\(=200\cdot85=17000\)

b: \(=\left(24-11\right)+\left(32-19\right)+\left(40-27\right)+...+\left(336-323\right)\)

\(=13\cdot\left[\left(336-24\right):8+1\right]=13\cdot40=520\)

c: \(=\left(5-2\right)+\left(8-4\right)+\left(11-6\right)+...+\left(140-92\right)\)

=3+4+5+...+48

Số số hạng là (48-3):1+1=45+1=46(số)

Tổng là: (48+3)*46/2=51*23=1173

d: \(=\left(300-285\right)+\left(295-278\right)+\left(290-271\right)+...+\left(100-5\right)+10\)

=15+17+19+...+95+10

Số số lẻ trong khoảng từ 15 đến 95 là:

(95-15):2+1=41(số)

Tổng của dãy số trên là:

10+(95+15)*41/2

=10+55*41

=2265

1)\(2^3.5+4^{15}:4^{13}+3^2.1^{100}=8.5+4^2+3^2.1=40+16+9=65\)

2)\(140+\left[25-\left(11-8^2\right)\right]=140+\left[25-\left(11-64\right)\right]=140+\left(25+53\right)=140+78=218\)

3)Ta có: 6*5 chia hết cho 5 vì có tận cùng là 5 

Để 6*5 chia hết cho 9 thì 6 + * + 5 = 11 + * phải chia hết cho 9  => * = 7 

thanks Minh Anh lan nua nhaaa ! minh da k roi do ^^

a)320 + ( 218-x)=475
             ( 218-x)=475-320
             ( 218-x)=155
                       x =218-155
                       x =63
b)315-6/x=275
          6/x=315-275
          6/x=40
            x=40.6
           x=240

c)4*(x-15)+32=64
  4*(x-15)        =64-32
  4*(x-15)        = 32
  4*(x-15)        =32:4
  4*(x-15)        =8 
      (x-15)        =8:4
      (x-15)        =2
       x               =2+15
       x               =17
 

M=8/3.2/5.3/8.10.19/92

=(8/3.3/8).(2/5.10).19/92

=1.4.19/2

=4.19/92

=19/23

N=5/7.5/11+5/7.2/11-5/7.14/11

=5/7.(5/11+2/11-14/11)

=5/7.  -7/11= -5/11

Q=(1/99+12/999 +123/9999).(1/2-1/3-1/6)

=(1/99+12/999+123/9999).(3/6+  -2/6+  -1/6)

=(1/99+12/999+123/9999). 0

=0

8/3 . 2/5 . 3/8 . 10 .19/92 trên 5/7 . 5/11 +5/7 .2/11 - 5/7.11/11

=16/15 .15/4 .19/92 trên 5/7(5/11 +2/11 -11/11)

= .4 .19/92 trên 5/7.(-4/11)

=19/2 trên -20/77

\(\frac{\frac{8}{3}.\frac{2}{5}.\frac{3}{8}.10.\frac{19}{92}}{\frac{5}{7}.\frac{5}{11}+\frac{5}{7}.\frac{2}{11}-\frac{5}{7}.\frac{11}{11}}\)

=\(\frac{\frac{2}{5}.10.\frac{19}{92}}{\frac{5}{7}.\left(\frac{5}{11}+\frac{2}{11}-1\right)}\)

=\(\frac{\frac{19}{23}}{\frac{-20}{77}}\)

=\(\frac{19}{23}.\frac{-77}{20}\)

=\(\frac{-1463}{460}\)