=1/4.5+1/5.6+1/6.7+...

c) Ta có: \(\dfrac{3}{5}+\dfrac{-5}{20}+\dfrac{30}{75}+\dfrac{-7}{4}\)

\(=\dfrac{3}{5}+\dfrac{2}{5}+\dfrac{-1}{4}+\dfrac{-7}{4}\)

\(=1-2=-1\)

Giải:

a)-1/12+4/3=-1/12+16/12=15/12=5/4

b)(-4/14-3/15)-(1/5-20/35-(-1)).7

=-17/35-22/35.7

=-17/35-22/5

=-171/35

c)3/5+-5/20+30/75+-7/4

=3/5+-1/4+2/5+-7/4

=(3/5+2/5)+(-1/4+-7/4)

=1+-2

=-1

d)5/6.-12/14+7/13

=-5/7+7/13

=-16/91

e)2/-9-5/-36-1/4

=-1/12-1/4

=-1/3

f)2/23+-5/12+7/18+21/23+-7/12

=(2/23+21/23)+(-5/12+-7/12)+7/18

=1+-1+7/18

=7/18

xcsxccsz

A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56

A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8

A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8

A = 1 + ( -1/2 + 1/2 ) + ( -1/3 + 1/3 ) + ( -1/4 + 1/4 ) + ( -1/5 + 1/5 ) + ( -1/6 + 1/6 ) + ( -1/7 + 1/7 ) - 1/8

A = 1 + 0 + 0 + 0 + 0 + 0 + 0 - 1/8

A = 1 - 1/8

A = 7/8

* Sửa đề tí nhé 

B = 3/2 - 5/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56

B = 3/1.2 - 5/2.3 + 7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8

B = 3 - 3/2 - 5/2 - ( -5/3 ) + 7/3 - 7/4 - 9/4 - ( -9/5 ) + 11/5 - 11/6 - 13/6 - ( -13/7 ) + 15/7 - 15/8

B = 3 - 3/2 - 5/2 + 5/3 + 7/3 - 7/4 - 9/4 + 9/5 + 11/5 - 11/6 - 13/6 + 13/7 + 15/7 - 15/8

B = 3 + ( -3/2 - 5/2 ) + ( 5/3 + 7/3 ) + ( -7/4 - 9/4 ) + ( 9/5 + 11/5 ) + ( -11/6 - 13/6 ) + ( 13/7 + 15/7 ) - 15/8

B = 3 + -4 + 4 + -4 + 4 + -4 + 4 - 15/8

B = 3 + 0 + 0 + 0 - 15/8

B = 3 - 15/8

B = 9/8

a) \(\frac{13}{7}-\frac{1}{2}\times\frac{13}{7}+\frac{3}{2}\times\frac{13}{7}\)

\(=\frac{13}{7}\times\left(1-\frac{1}{2}+\frac{3}{2}\right)\)

\(=\frac{13}{7}\times2\)

\(=\frac{26}{7}\)

b) \(\frac{1}{15}\times\left(\frac{3}{7}+\frac{5}{19}\right)+\frac{3}{7}\times\left(\frac{5}{19}-\frac{1}{15}\right)\)

\(=\frac{1}{15}\times\frac{3}{7}+\frac{1}{15}\times\frac{5}{19}+\frac{3}{7}\times\frac{5}{19}-\frac{3}{7}\times\frac{1}{15}\)

\(=\frac{5}{19}\times\left(\frac{1}{15}+\frac{3}{7}\right)\)

\(=\frac{5}{19}\times\frac{52}{105}\)

\(=\frac{52}{399}\)

c) \(\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+...+\frac{5}{9900}\)

\(=5\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{99\times100}\right)\)

\(=5\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=5\times\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=5\times\frac{49}{100}\)

\(=\frac{49}{20}\)

Lần sau nên đăng ít thôi

a) \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

=> \(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

=> \(A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66

       = (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)

       = 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)

       = 25/66

b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

       = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

       = (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)

       = 1/1 - 1/7 = 6/7

c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21

   C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)

   C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]

   C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)

   C = 1

Dễ nhưng dài quá !

a) 43/20 + 17/6 : ( 150/240 + 210/240 )

=    43/20 + 17/6 :  360/240

=    43/20 + 17/6 : 3/2

=    43/20 + 34/18

=     774/360 + 612/360

=   1386/360

=  77/20

b)

=  ( 5/30 + 3/30 + 2/30 ) : ( 5/30 + 3/30 - 2/30 )

=  10/30   :    0

=  1/3   :   0

=1/3

Đó là cách giải chi tiết va dễ hiểu nhất đó     ^ - ^