C

A

C nhé Khi ko tính số 0 trên dãy số trên thì ta có quy luật tổng hai số đằng sau sẽ bằng số ở phía trước (VD 1+2=3;3+2=5;3+5=8;8+5=13;...) mình chúc bạn học tốt nhé

`a)1 4/23 + ( 5/21-4/23)+16/21-1/2`

`=27/23+5/21-4/23+16/21-1/2`

`=(27/23-4/23)+(5/21+16/21)-1/2`

`=23/23+21/21-1/2`

`=1+1-1/2`

`=2-1/2`

`=4/2-1/2`

`=3/2`

___

`b)75%-(5/2+5/3)+(-1/2)^3`

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

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

`=(6/8-20/8-1/8)+5/3`

`=-15/8+5/3`

`=-45/24+40/24`

`=-5/24`

___

`c)-3/4(-55/9).8/11`

`=-3/4.(-40/9)`

`=-10/3`

__

`d)-3/8 . 6/13 + 7/13 . (-3/8) + 1 3/8`

`= -3/8 . (6/13 + 7/13) + 11/8`

`= -3/8 . 13/13 + 11/8`

`= -3/8 .1 + 11/8`

`= -3/8 + 11/8`

`= 8/8`

`=1`

A=55/11.16+55/16.21+...+55/36.41

A=11x(1/11−1/16+1/16−1/21+...+1/36−1/41)

A=11x(1/11−1/41)

A=11x30/451

A=30/41

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

a. (21 - 1) x (21 - 2) x (21 - 3) x ... x (21 - 21)

= 20 x 19 x 18 x ... x 0

= 0

b. 3 x 27 x 8 + 4 x 35 x 6 + 2 x 38 x 12

= (3 x 8) x 27 + (4 x 6) x 35 + (2 x 12) x 38

= 24 x 27 + 24 x 35 + 24 x 38

= 24 x (27 + 35 + 38)

= 24 x100

= 2400

c. A = (1001 + 1002 + 1003 +... + 2009) x (360 x 87 - 360 x 32 - 360 x 55)

       = (1001 + 1002 + 1003 + ... + 2009) x [360 x (87 - 32 - 55)]

       = (1001 + 1002 + 1003 + ... + 2009) x (360 x 0)

       = (1001 + 1002 + 1003 + ... + 2009) x 0

        = 0 

Mình cảm ơn bạn nhiều :!!!

\(1,=38-42+14-25+27+15=27\)

\(2,=12+21-23+21-10=21\)

\(3,=57-725-605+53=-1220\)

\(4,=55+45+15-15+55-45=110\)

\(\text{1.(38-42+14)-(25-27-15)}\\ =38-42+14-25+27+15\\ =-4-11+42\\ =27\)

\(\text{2.(12+21)-(23-21+10)}\\ =12+21-23+21-10\\ =33+44-10=67\)

X+21+(-18)+(-40)=x+21-18-40=x-37

-55-(y+

a) x + 21 + (-18) + (-40)

= x + 21 - 18 - 40

= x - 37

b) -55 - (y + 20) - (-55)

= -55 -y - 20 + 55

= - y - 20

c) -(a - b) + ( a - c -d + b )

= - a + b + a -c - d +b 

= 2b - c - d

-55-(y+20)-(-55)=-55-y-20+55=0-y-20=-(y+20)

-(a-b)+(a-c-d+b)

=2b-c-d

Lời giải:
Gọi tổng trên là $A$.

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

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

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

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

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

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

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

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

\(\dfrac{55}{11}\cdot6+\dfrac{55}{16}\cdot21+\dfrac{55}{21}\cdot26+\dfrac{55}{26}\cdot31+\dfrac{55}{31}\cdot36+\dfrac{55}{36}\cdot41=30+\dfrac{1155}{16}+\dfrac{1430}{21}+\dfrac{1705}{26}+\dfrac{1980}{31}+\dfrac{2255}{36}=\dfrac{12186720}{406224}+\dfrac{29324295}{406224}+\dfrac{27661920}{406224}+\dfrac{26638920}{406224}+\dfrac{25945920}{406224}+\dfrac{25445420}{406224}=\dfrac{147203195}{406224}\)