a) 5/9 x 12/25 = 4/15

b) 12/11 : 36/55 = 5/3

c) 9/55 x 22 = 18/5

d) 144/7 : 36 = 4/7

a) 5/9 x 12/25 = 4/15

b) 12/11 : 36/55 = 5/3

c) 9/55 x 22 = 18/5

d) 144/7 : 36 = 4/7

A=55*[(1/11*16) * 1/5 + (1/16*21) * 1/5 + (1/21*26) * 1/5 + (1/26*31) * 1/5 + (1/31*36) * 1/5 + (1/36*41) * 1/5 ]

 = 55* [ (1/11*16) + (1/16*21) + (1/21*26) + (1/26*31)  + (1/31*36)  + (1/36*41) ] * 1/5

 = 55 * [ 1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31+1/31-1/36+1/36-1/41) * 1/5 

 = 55 * ( 1/11 - 1/41 ) * 1/5

 = 30/41

5/9 x 12/25 = 4/15

12/11 : 36/ 55 = 5/3

9/55 x 22 = 18/5 

144/7 : 36 = 4/7

4 phần 15

5 phần 3

18 phần 5

4 phần 7

\(A=\frac{55}{11\cdot16}+\frac{55}{16\cdot21}+\frac{55}{21\cdot26}+...+\frac{55}{36\cdot41}\)

\(=\frac{55}{5}\cdot\left(\frac{16-11}{11\cdot16}+\frac{21-16}{16\cdot21}+\frac{26-21}{21\cdot26}+...+\frac{41-36}{36\cdot41}\right)\)

\(=11\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{26}-\frac{1}{31}+...+\frac{1}{36}-\frac{1}{41}\right)\)

\(=11\cdot\left(\frac{1}{11}-\frac{1}{41}\right)=11\cdot\frac{41-11}{11\cdot41}=\frac{30}{41}\).

Đối với các bạn dễ nhưng đối với bạn ấy khó !!!!

chưa học nên chưa BÍT

\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)

\(3A=3\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right)\)

\(3A=\frac{3}{4}+\frac{3}{12}+\frac{3}{36}+\frac{3}{108}+\frac{3}{324}+\frac{3}{927}\)

\(3A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)

\(2A=3A-A\)

\(2A=\left(\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\right)-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right)\)

\(2A=\frac{3}{4}-\frac{1}{927}\)

\(2A=\frac{729-1}{972}=\frac{728}{972}=\frac{182}{243}\)

\(A=\frac{182}{243}:\frac{1}{2}\)

\(A=\frac{364}{243}\)

A=1/4+1/12+1/36+1/108+1/324+1/972

=243/972+81/972+27/972+9/972+3/972+1/972

=364/972

=91/243

a) {132 - [116- (16 - 8)]:2}.5

= [132 - (116 - 8): 2] .5

= (132 - 108 : 2). 54

= (132 - 54).5

= 78.5 = 390

b) 36: {136 : 200 - (12+ 8. 20)]}

= 36: {336 : [200 - ( 12 + 160)]}

= 36 : [336 : ( 200 - 172)

= 36 : ( 336 : 28) = 3

c) 86 - [15. (64 - 39): 75+11] 

= 86 - (15.25 : 75 + 11) 

= 86 - ( 5 + 11) 

= 70

d)  55 - [ 49 - ( 2 3 . 17 - 2 3 . 14 ) ]

= 55 - 49 - 2 3 . 3

= 55- ( 49 - 24)

= 30

Bạn ơi ở chỗ trước số 200 có dấu này [mà

a) {132 – [116 – (16 – 8)]:2}.5

= [132 – (116 – 8): 2] .5

= (132 – 108 : 2). 5

= (132 –54).5

= 78.5 = 390

b) 36: {136 : 200 – (12+ 8. 20)]}

= 36: {336 : [200 – ( 12 + 160)]}

= 36 : [336 : ( 200 – 172)

= 36 : ( 336 : 28)

= 36 : 12 = 3

c) 86 – [15. (64 - 39): 75+11]

= 86 – (15.25 : 75 + 11)

= 86 – ( 5 + 11)

= 70.

d) 55 – [49 – (2³ . 17 – 2³.14)]

= 55 – (49 – 2³ .3)

= 55 – ( 49 – 24)

= 30

Lời giải:
Gọi tổng trên là $A$.

$A=11\times (\frac{5}{11\times 16}+\frac{5}{16\times 21}+\frac{5}{21\times 26}+....+\frac{5}{36\times 41})$

$=11\times (\frac{16-11}{11\times 16}+\frac{21-16}{16\times 21}+\frac{26-21}{21\times 26}+....+\frac{41-36}{36\times 41})$

$=11\times (\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{36}-\frac{1}{41})$

$=11\times (\frac{1}{11}-\frac{1}{41})=1-\frac{11}{41}=\frac{30}{41}$

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)

\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)

\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=9-\left(1-\frac{1}{10}\right)\)

\(=9-\frac{9}{10}=\frac{81}{10}\)