\(A=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+.......\frac{1}{13x15}=\frac{1}{2}x\frac{2}{1x3}+\frac{2}{3x5}.......+\frac{2}{13x15}\)

\(A=\frac{1}{2}x\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}\right)\)

Còn lại em nhân giống ở trên nhé

Đặt A = 1/15 + 1/35 + ... + 1/3135 

       A = 1/3.5 + 1/5.7 + ... + 1/55.57

     2A =  2/3.5 + 2/5.7 + ... + 2/55.57 

    2A = 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/55 - 1/57 

    2A = 1/3 - 1/57 = 6/19 

      A = 3/19 

thanks các bn

a) \(\frac{1}{3}+\frac{5}{6}:\left(x-2\frac{1}{5}\right)=\frac{3}{4}\)

=> \(\frac{1}{3}+\frac{5}{6}:\left(x-\frac{11}{5}\right)=\frac{3}{4}\)

=> \(\frac{5}{6}:\left(x-\frac{11}{5}\right)=\frac{3}{4}-\frac{1}{3}\)

=> \(\frac{5}{6}:\left(x-\frac{11}{5}\right)=\frac{5}{12}\)

=> \(x-\frac{11}{5}=\frac{5}{6}:\frac{5}{12}\)

=> \(x-\frac{11}{5}=2\)

=> \(x=2+\frac{11}{5}\)

=> \(x=\frac{21}{5}\)

thanks bn

1/15 +1/35 + 1/63 + ... + 1/3135

= 1/3*5 + 1/5*7 + 1/7*9 + ... + 1/55*57

= 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/55 - 1/57

= 1/3 - 1/57

= 18/57

1/3 + 1/6 + 1/10 +  ... + 1/x(x + 1)*2 = 2009/2011

=> 2/6 + 2/12 + 2/20 + ... + 2/x(x + 1)*2 = 2009/2011

=> 2(1/6 + 1/12 + 1/20 + ... + 1/x(x + 1)) = 2009/2011

=> 2(1/2*3 + 1/3*4 + 1/4*5 + ... + 1/x(x + 1)) = 2009/2011

=> 2(1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/x - 1/x + 1)  = 2009/2011

=> 2(1/2 - 1/x + 1) = 2009/2011

=> 1/2 - 1/x + 1 = 2009/4022

=> 1/x + 1 = 1/2011

=> x + 1 = 2011

=> x = 2010

vậy-

\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+.......+\dfrac{1}{x\cdot\left(x+1\right)}=\dfrac{122}{123}\)

\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{122}{123}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{122}{123}\)

\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{123}\)

\(\Leftrightarrow x=122\)

Có ai biết không giúp tôi với nhé 

a) 0,5 + ( x - 15/2 ) : 1/2 = 9/2

<=>      (x - 15/2 ): 1/2   = 9/2 - 0,5

<=>      (x - 15/2)  : 1/2   = 4 

<=>        (x - 15/2)          = 4 . 1/2 

<=>        x - 15/2            = 2

<=>        x                     = 2 + 15/2 

<=>        x                     = 19/2  

b) 2012x - 2010x  = 2014 

( 2012 - 2010 ) .x  = 2014 

  2x                     = 2014 

   x                      = 2014 :2  

   x                      = 1007  

cảm ơn

Tìm x biết:

a,x-1/2 =2/15

x=2/15 + 1/2

x =19/30

Vậy x =19/30

b,5 và 3/4 +x =15 - 2 và 1/2

23/4 + x  =27/2

x =27/2 - 23/4

x=31/4

Vậy x =31/4

c,x : 14,1 =0,25

x =0,25.14,1

x=3,525

Vậy x = 3.525

d,x + 1/2.1/3 =3/4

x + 1/6 =3/4

x =3/4 - 1/6

x =7/12

Vậy x = 7/12

a)\(x=\frac{2}{15}+\frac{1}{2}=\frac{4+1}{15x2}=\frac{5}{30}=\frac{1}{6}\)

b)anh chưa hiểu lắm hỗn số à em

c)\(x=\frac{1}{4}x\frac{141}{10}=\frac{141}{40}=3,525\)

d)\(x+\frac{1}{6}=\frac{3}{4}\)

suy ra: \(x=\frac{3}{4}-\frac{1}{6}=\frac{18-4}{24}=\frac{14}{24}=\frac{7}{12}\)

a x - 1\2 = 2\15

x            =2\15 + 1\2

x            =19\30

b 23\4 + x =27\2

x               =27\2-23\4

x                =31\4

c x :14,1=0,25

x            =0,25 x 14 ,1

x            =3,525

d x +1\2 .1\3 =3\4

x+1\6 =3\4

x        =3\4-1\6

x        =7\12

- Giải:

a) 29 + ( 132 + 868 ) + ( 237 + 763 )

= 29 + ( 1000 + 1000 )

= 29 + 2000 = 2029

b) 652 + 327 + 148 + 15 + 73

= ( 652 + 148 ) + ( 327 + 73 ) + 15

= ( 800 + 400 ) + 15 =  1215

-------Phần còn lại nhờ mấy bn khác lm hộ nhé-------

a) 29 + 132 + 237 + 868 + 763
=  29 + (132 + 868) + (237 + 763)
=  29 + 1000 + 1000
=  2029
b) 652 + 327 + 148 + 15 + 73
=  (652 + 148) + (327 + 73) + 15
=  800 + 400 + 15
=  1215
c) 35 . 24 + 35 . 38 + 65 . 75 + 45 . 65
=  35(24 + 38) + 65(75 + 45)
=  35 . 62 + 65 . 120
=  5 . 7 . 2 . 31 + 65 . 12 . 10
=  10 . 7 . 31 + 65 . 12 .10
=  10(7 . 31 + 65 . 12)
=  10(217 + 780)
=  10 . 997
=  9970
d) 3 . 25 + 4 . 37 . 6 + 2 . 38 . 12
=  3 . 25 + 4 . 37 . 2 . 3 + 2 . 38 . 12
=  3 . 25 + 12 . 37 . 2 + 2 . 38 . 12
=  3 . 25 + 12 . 2(37 + 38)
=  3 . 25 + 12 . 2 . 75
=  3 . 25 + 12 . 2 . 3 . 25
=  3 . 25(1 + 12 . 2)
=  3 . 25 . 25
=  1875

a)29+132+237+868+763

=(132+868)+(237+763)+29

=     1000   +   1000    +29

=      2029

b)652+327+148+15+73

=(652+148)+(327+73)+15

=800+400+15

=1215

c)35x24+35x38+65x75+45x65

=35x(24+38)+65x(75+45)

=35x62+65x120

=2170+7800

=9970

d)3x25+4x37x6+2x38x12

=3x25+24x37+24x38

=3x25+24(37+38)

=75+24x75

=75(1+24)

=75x25

=1875

a) \(5+3^{x+1}=86\)

\(=>3^{x+1}=86-5\)

\(=>3^{x+1}=81=3^4\)

\(=>x+1=4\) ( cùng cơ số )

\(=>x=4-1\)

\(=>x=3\)

b) \(15:\left(x+2\right)=\left(3^3+3\right):10\)

\(=>15:\left(x+2\right)=\left(27+3\right):10\)

\(=>15:\left(x+2\right)=30:10=3\)

\(=>x+2=15:3\)

\(=>x+2=5\)

\(=>x=5-2\)

\(=>x=3\)

c) \(\left(9x+2\right).4=80\)

\(=>9x+2=80:4\)

\(=>9x+2=20\)

\(=>9x=20-2\)

\(=>9x=18\)

\(=>x=18:9\)

\(=>x=2\)

d) \(\left(245-x\right)+7^2=14\)

\(=>\left(245-x\right)+14=14\)

\(=>245-x=14-14\)

\(=>245-x=0\)

\(=>x=245-0\)

\(=>x=245\)

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