=1/1.3.5+1/3/5/7+1/5.7.9+......+1/17/19/21

=1/4.(5-1/1.3.5+7-3/3.5.7+.....+21-17/17/19/21

=1/4.(5/1.3.5-1/1.3.5+7/3.5.7-3/3.5.7+.....+21/17.19.21-17/17.19.21

=1/4.(1/1.3-1/3.5+1/3.5-1/5.7+.....+1/17.19-1/19.21)

=1/4.(1/3.1/21.17)

=1/4.3200/9603

= 800/9603

            Chúc bạn học tốt^^

Đặt \(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{17.19.21}\)

\(\Rightarrow4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+...+\frac{4}{17.19.21}\)

\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{17.19}-\frac{1}{19.21}\)

\(=\frac{1}{1.3}-\frac{1}{19.21}=\frac{44}{133}\)

\(\Rightarrow A=\frac{44}{133}\div4=\frac{11}{133}\)

1)\(\frac{1}{7}\).(\(\frac{1}{3}\)+\(\frac{1}{2}\)-1)

=\(\frac{1}{7}\).\(\frac{-1}{6}\)

=\(\frac{-1}{42}\)

2)\(\frac{3}{5}\).(\(\frac{7}{9}\)+\(\frac{2}{9}\)+1)

=\(\frac{3}{5}\).2=\(\frac{6}{5}\)

3)=21.\(\frac{1}{7}\)-21.\(\frac{1}{5}\)+21.\(\frac{19}{21}\)

=3-\(\frac{21}{5}\)+19

=\(\frac{89}{5}\)

cảm ơn bạn nhé

Tôi cũng làm thế đấy cơ mà chả hợp lí gì cả cũng hoang mang lắm này -.-

Mk tk cho nhé!!!

`@` `\text {Ans}`

`\downarrow`

`1)`

`5/7*37 13/23 - 51 13/23*5/7`

`= 5/7* (37 13/23 - 51 13/23)`

`= 5/7* (-14)`

`= -10`

`2)`

`-2/3 +1/3+0,5+2 1/2`

`= -2/3 + 1/3 + 1/2 + 5/2`

`= (-2/3+1/3) + (1/2+5/2)`

`= -1/3 + 3`

`=8/3`

`3)`

`-0,5+2/3+1/2`

`= -1/2 + 2/3 + 1/2`

`= (-1/2 + 1/2) + 2/3`

`= 2/3`

`4)`

`(8+2 1/3-3/5) -(5+0,4)-(3 1/2 -2)`

`= 8+ 7/3 - 3/5 - 5 - 0,4 - 7/2 + 2`

`= (8+2-5) + (-3/5 - 2/5) + (7/3 - 7/2)`

`= 5 - 1 - 7/6`

`= 4 - 7/6 = 17/6`

`5)`

`(2/9-7/12):3/4+(16/9-5/12):3/4`

`= (2/9 - 7/12) \times 4/3 + (16/9 - 5/12) \times 4/3`

`= 4/3 *(2/9 - 7/12 + 16/9 - 5/12)`

`= 4/3 * [(2/9 + 16/9) + (-7/12 - 5/12)]`

`= 4/3 * ( 2 - 1)`

`= 4/3 * 1 = 4/3`

`6)`

`-(2021.0,7+19,75) +0,7- (8-19,75)`

`= -2021*0,7 -19,75 + 0,7 - 8 + 19,75`

`= 0,7*(-2021 + 1) - 8`

`= -1414-8`

`= -1422`

`7)`

`15/34+7/21+19/34-20/15`

`= (15/34 + 19/34) + 7/21 - 20/15`

`= 1 + 7/21 - 20/15`

`= 4/3 - 20/15 =0`

`8)`

`2 5/6+1/6:(-5/8)`

`= 17/6 + (-4/15)`

`= 77/30`

`9)`

`(-2)^2 +2/9. (4/5-2/3)`

`= 4 + 2/9*2/15`

`= 4+4/135`

`= 544/135`

`10)`

`(-1/5+3/7):5/4+(-4/5+4/7):5/4`

`= (-1/5+3/7) * 4/5 + (-4/5+4/7) * 4/5`

`= 4/5*(-1/5 +3/7-4/5+4/7)`

`= 4/5*[(-1/5-4/5)+(3/7+4/7)]`

`= 4/5* (-1+1)`

`= 4/5*0=0`

`11)`

`2022,2021 . 1954,1945+ 2022,2021 . (-1954,1945)`

`= 2022,2021 * [1954,1945 + (-1954,1945)]`

`= 2022,2021*0 `

`= 0`

`12)`

`-5,2 .72 +69,1 +5,2 . (-28)+(-1,1)`

`= -5,2*72 + 69,1 - 5,2*28 - 1,1`

`= -5,2*(72+28) + (69,1 - 1,1)`

`= -5,2*100 + 68`

`= -520 + 68`

`= -452`

`13)`

`(7 -1/2-3/4) : (5-1/4-5/8)`

`= 23/4 \div 33/8`

`=46/33`

`14)`

`(8+ 2 1/3 -3/5) -(5+0,4) -( 3 1/3 - 2)`

`= 8+ 2 1/3 - 3/5 - 5 - 0,4 - 3 1/3 + 2`

`= (8+2-5) + (2 1/3 - 3 1/3) - (0,6 + 0,4) `

`= 5 - 1 - 1`

`= 3`

help lười tính quá

2: \(=\dfrac{-1}{3}+3=\dfrac{8}{3}\)

3: =1/2-1/2+2/3=2/3

5: \(=\dfrac{4}{3}\left(\dfrac{2}{9}-\dfrac{7}{12}+\dfrac{16}{9}-\dfrac{5}{12}\right)=\dfrac{4}{3}\)

12: \(=5.2\left(-72-28\right)+68=-520+68=-452\)

13: \(\dfrac{23}{4}:\dfrac{33}{8}=\dfrac{46}{33}\)

a) 1-3+5-7+9-12+15-18

= (1+ 9) - (3+7) + (5+15) - (12+18) 

= 10 - 10 + 20 - 30 = -10.

b) (-2)+5-7+9-11+13-15+19-21

= 5 - 11 - 2 -2 = 5 - (11+2+2)

= 5 - 15 = -10 

Bài 1: 

a) Ta có: 1-3+5-7+9-12+15-18

=(1+9)-(3+7)+(5+15)-(12+18)

=10-10+20-30

=-10

b) Ta có: \(\left(-2\right)+5-7+9-11+13-15+19-21\)

\(=3+2+2+4-21\)

\(=5+6-21\)

=11-21=-10

Bài 5) Tính giá trị của biểu thức

a) A=1.2+2.3+3.4+...+9.10

b) B=3.4+4.5+5.6+...+198.199+199.200

c) C=1.2.3+2.3.4+3.4.5+...+8.9.10

d) D=31.32.33+32.33.34+...+58.59.60

e) E=1.3+3.5+5.7+...+95.97+97.99

f) F=51.53+53.55+...+153.155+155.157

g) G=1.3.5+3.5.7+...+15.17.19+17.19.21

h) H=2.4+4.6+6.8+...+96.98+98.100

Cần chi tiết hum bẹn

a) = 76/35 ; 37/9

b) 143/40 ; 19/15

c) 2/3 ; 42/5

d) 21/4 ; 4/7 

a, 11/7 + 3/5

= \(\dfrac{11x5}{7x5}+\dfrac{3x7}{5x7}=\dfrac{55}{35}+\dfrac{21}{35}=\dfrac{76}{35}\)

4 + 1/9

= \(\dfrac{4}{1}+\dfrac{1}{9}=\dfrac{4x9}{1x9}+\dfrac{1x1}{9x1}=\dfrac{36}{9}+\dfrac{1}{9}=\dfrac{37}{9}\)

b, 21/5 - 5/8

= \(\dfrac{21x8}{5x8}-\dfrac{5x5}{8x5}=\dfrac{168}{40}-\dfrac{25}{40}=\dfrac{143}{40}\)

2 - 11/15

=\(\dfrac{2}{1}-\dfrac{11}{15}=\dfrac{30}{15}-\dfrac{11}{15}=\dfrac{19}{15}\)

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