\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)

\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)

\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)

\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)

\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)

2.

a, x-13=-46

=>x=(-46)+13

=>x=33

b, 4x-6=22

=>4x=22+6

=>4x=28

=>x=28:4

=>x=7

3.

a, 32=2⁵

48=2⁴.3

=>ƯCLN(32,48)=2⁴=16

16=2⁴

72=2³.3²

=>ƯCLN(16,72)=2³=8

b,

24=2³.3

60=2².3.5

=>BCNN(24,60)=2³.3.5=120

72=2³.3²

180=2².3².5

=>BCNN(72,180)=2³.3².5=360

a) x - 13  =  -   46 

    x         =  - ( 46 + 13 )                                

    x         =  - 59   

Chắc vậy

Ai nhanh nhất k nhiều nhất nhé

Bài này đề bài là tìm x

98775 - 32 x 85

=98775 -2720

=96055

 67500 - 24 x 236

= 67500 -5664

=61836

 568 + 101598 : 287

= 568 +354

=922

6875 + 980 -180  

=7855 -180 

=7675

\(\dfrac{2}{5}+\dfrac{3}{10}-\dfrac{1}{2}\)

\(=\dfrac{7}{10}-\dfrac{1}{2}\)

= \(\dfrac{1}{5}\)

\(\dfrac{8}{11}+\dfrac{8}{33}x\dfrac{3}{4}\)

\(=\dfrac{8}{11}+\dfrac{2}{11}\)

\(=\dfrac{10}{11}\)

\(\dfrac{7}{9}x\dfrac{3}{14}:\dfrac{5}{8}\)

\(=\dfrac{1}{6}:\dfrac{5}{8}\)

\(=\dfrac{1}{6}x\dfrac{8}{5}\)

\(=\dfrac{8}{30}\)

\(=\dfrac{4}{15}\)

\(\dfrac{5}{12}-\dfrac{7}{32}:\dfrac{21}{16}\)

\(=\dfrac{5}{12}-\dfrac{7}{32}x\dfrac{16}{21}\)

\(=\dfrac{5}{12}-\dfrac{1}{6}\)

\(=\dfrac{5}{12}-\dfrac{2}{12}\)

\(=\dfrac{3}{12}=\dfrac{1}{4}\)

2^2.(x+3^2)-5=55
           4.(x+9)=55+5=60
     (x+9)=60:4=15
           x=15-9=6
             vậy x=6

\(3^2.5-2^2.7+83\)

\(=9.5-4.7+83\)

= \(45-28+83\)

= \(100\)

180 : ( 18 x 5 )

= 180 : 90

= 2

b) 240 : ( 2 x 3 x 4 )

= 240 : 24

= 10

c) 4400 : ( 22 x 35 ) 

= 4400 : 770

= \(\dfrac{40}{7}\)

\(22.\left(x+32\right)-5=55.179^0\\ 22.\left(x+32\right)-5=55.1\\ 22.\left(x+32\right)-5=55\\ 22.\left(x+32\right)=55+5\\ 22.\left(x+32\right)=60\\ x+32=60:22\\ x+32=\dfrac{30}{11}\\ x=\dfrac{30}{11}-32\\ x=\dfrac{-322}{11}\)

\(22.\left(x+32\right)-5=55.179^0\)

=>22.(x+32)-5=55.1

=>22.(x+32)-5=55

=>22.(x+32)=55+5

=>22.(x+32)=60

=>x+32=60:22

=>x+32=\(\dfrac{30}{11}\)

=>x=\(\dfrac{30}{11}-32\)

\(=>x=-\dfrac{322}{11}\)

Vậy............

`22(x+32)-5=55. 179^0`

`=>22(x+32)-5=55.1`

`=>22(x+32)-5=55`

`=> 22(x+32)=55+5`

`=>22(x+32)=60`

`=>x+32=60:22`

`=>x+32=30/11`

`=>x=30/11-32`

`=>x=-322/11`

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