\(\frac{1}{2\cdot x}-2021-\frac{1}{4}-\frac{1}{12}-\frac{1}{24}-...-\frac{1}{222}=\frac{6}{11}\)

\(\frac{1}{2\cdot x}-2021-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{222}\right)=\frac{6}{11}\)

....

Cái dãy \(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{222}\) nó không có quy luật, không tính được

Sửa đề\(\frac{1}{2x-2021}-\frac{1}{4}-\frac{1}{12}-\frac{1}{24}-...-\frac{1}{220}=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{220}\right)=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\frac{1}{2}\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\frac{1}{2}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{10}-\frac{1}{11}\right)=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\frac{1}{2}\left(1-\frac{1}{11}\right)=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\frac{1}{2}.\frac{10}{11}=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}-\frac{5}{11}=\frac{6}{11}\)

=> \(\frac{1}{2x-2021}=1\)

=> 2x - 2021 = 1

=> 2x = 2022

=> x = 1011

Vậy x = 1011

Nhanh nha các bạn giúp mình

Tính bằng cách hợp lí nếu có thể

A) 21 . 35 - 3 . 25

B)48 . (-21) + (-142) . (-24)

C)77 - 11 . (30+7

1)    243 - 9.(x+8) = 45

          9. (x+8)     = 243 -45 

           9. (x+8)    = 198

               x+8      = 22

                 x        =14

2)     m` ko hiểu đề bài

thứ ba

thứ 3

Bài 1 tính nhanh

A) 21 . 35 - 3 . 25

B)48 . (-21) + (-142) . (-24)

C)77-11 . (30+7)

D)47.(45-15) - 47.(45+15)

Bài 2 tìm x

A) 17-(2+x)=3

B) (^+x) - (17-23) = -11

C)4 .x -15 = -75-x

D) 72-3.x=5.x+8

E)2.(X+1) +3.(x-2)=x-4

                          Dấu chấ

21.35-3.25
=3.7.35-3.25
=3.(7.35-25)
=3.(245-25)
=3.220
=660

Bài 2 

a,17-(2+x)=3

        (2+x)=17-3

        (2+x)=14

               x=14-2

               x=12

b,Bạn ghi ^ là thế nào

Bài 1:

a)\(21.35-3.25=3.7.7.5-3.5.5=3.5.\left(7.7-5\right)=15.44=660\)

b) \(48.\left(-21\right)+\left(-142\right).\left(-24\right)\)

\(=\left(-2\right).\left(-24\right).\left(-21\right)+\left(-2\right).71.\left(-24\right)\)

\(=\left(-2\right).\left(-24\right).\left(-21+71\right)=48.50=2400\)

c)\(............\)

d)\(=47.\left(45-15-45-15\right)=47.\left(-30\right)=-1410\)

Bài 2:

a)\(17-\left(2+x\right)=3\\ =>2+x=14=>x=12\)

b) ko rõ đề

c)\(4x-15=-75-x\)

\(=>4x+x=-75+15\)

\(=>5x=-60=>x=-12\)

d)\(72-3x=5x+8\)

\(=>-3x-5x=8-72\)

\(=>-8x=-64=>x=8\)

e)\(2\left(x+1\right)+3.\left(x-2\right)=x-4\)

\(=>2x+2+3x-6=x-4\)

\(=>2x+3x-x=-4+6-2\)

\(=>4x=0=>x=0\)

CẬU CS THỂ THAM KHẢO BÀI ALMF TRÊN ĐÂY Ạ. HỌC TỐT NHA:>

Ta có \(\dfrac{2}{1\cdot5}+\dfrac{2}{5\cdot9}+\dfrac{2}{9\cdot13}+...+\dfrac{2}{x\left(x+4\right)}=\dfrac{56}{113}\)

\(\dfrac{1}{2}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{x\left(x+4\right)}\right)=\dfrac{56}{113}\)

\(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{56}{113}:\dfrac{1}{2}\)

\(1-\dfrac{1}{x+4}=\dfrac{112}{113}\)

\(\dfrac{1}{x+4}=1-\dfrac{112}{113}=\dfrac{1}{113}\)

x + 4 = 113 ⇒ x = 109

\(\dfrac{2}{1.5}+\dfrac{2}{5.9}+...+\dfrac{2}{x\left(x+4\right)}=\dfrac{56}{113}\)

Xét: \(A=\dfrac{2}{1.5}+\dfrac{2}{5.9}+...+\dfrac{2}{x\left(x+4\right)}\)

\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x-4}-\dfrac{1}{x}+\dfrac{1}{x}-\dfrac{1}{x+4}\right)\)

\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{x+4}\right)\)

Với \(A=\dfrac{56}{113}\) thì

 \(\dfrac{1}{2}.\left(1-\dfrac{1}{x+4}\right)=\dfrac{56}{113}\)

\(\left(1-\dfrac{1}{x+4}\right)=\dfrac{112}{113}\)

\(\dfrac{1}{x+4}=\dfrac{1}{113}\)

\(x=109\)

Bài 1:

a) 8² . 2² = 64 . 4 = 256

b) 2⁵. 4 = 2⁵. 2²= 2⁵⁺² = 2⁷

c) 9⁴. 243 = 9⁴. 3⁵=(3²)⁴.3⁵=3⁸.3⁵=3⁸⁺⁵=3¹³