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6 tháng 7 2017

a, sai đề

b, \(\dfrac{1}{21}+\dfrac{1}{28}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\Rightarrow\dfrac{1}{42}+\dfrac{1}{56}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{1}{9}\) ( nhân cả 2 vế với \(\dfrac{1}{2}\) )

\(\Rightarrow\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{1}{9}\)

\(\Rightarrow\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{9}\)

\(\Rightarrow\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{1}{9}\)

\(\Rightarrow\dfrac{1}{x+1}=\dfrac{1}{18}\Rightarrow x+1=18\Rightarrow x=17\)

Vậy x = 17

6 tháng 7 2017

Câu a thiếu đề rồi bạn ơi mik giải câu b đây:

\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\dfrac{2}{42}+\dfrac{2}{56}+\dfrac{2}{72}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\dfrac{2}{6.7}+\dfrac{2}{7.8}+\dfrac{2}{8.9}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(2\left(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+....+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2}{9}\)

\(2\left(\dfrac{1}{6}-\dfrac{1}{x+2}\right)=\dfrac{2}{9}\)

\(\dfrac{1}{6}-\dfrac{1}{x+2}=\dfrac{2}{9}:2\)

\(\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{1}{9}\)

\(\dfrac{1}{x+1}=\dfrac{1}{6}-\dfrac{1}{9}\)

\(\dfrac{1}{x+1}=\dfrac{1}{18}\)

\(\Rightarrow x+1=18\Rightarrow x=17\)

Vậy x = 17

6 tháng 7 2017

câu a đề sai

6 tháng 7 2017

đề khó hiểu????????????

6 tháng 5 2017

a) Vì \(\dfrac{x+5}{3}\)= \(\dfrac{x-6}{7}\) nên 7(x+5) = 3(x-6)

=> 7x+ 35 = 3x - 18

7x - 3x = -18 -35

4x = -53

x = -53:4

x = \(\dfrac{-53}{4}\)

20 tháng 4 2017

các bạn phại đổi kiểu chữ để làm bài này (VNI) , (TELEX)

20 tháng 4 2017

vni

7 tháng 5 2018
https://i.imgur.com/KT76KfI.jpg

b: \(\Leftrightarrow x-10\left(\dfrac{2}{11\cdot13}+\dfrac{2}{13\cdot15}+...+\dfrac{2}{53\cdot55}\right)=\dfrac{3}{11}\)

\(\Leftrightarrow x-10\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{53}-\dfrac{1}{55}\right)=\dfrac{3}{11}\)

\(\Leftrightarrow x-10\cdot\dfrac{4}{55}=\dfrac{3}{11}\)

=>x=3/11+20/55=3/11+4/11=7/11

c: \(\Leftrightarrow\left(\dfrac{x-1}{99}-1\right)+\left(\dfrac{x-2}{98}-1\right)+\left(\dfrac{x-5}{95}-1\right)=\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{95}\)

\(\Leftrightarrow x-100=1\)

hay x=101

29 tháng 3 2017

\(x-\dfrac{20}{11.13}-\dfrac{20}{13.15}-\dfrac{20}{15.17}-...-\dfrac{20}{53.55}=\dfrac{3}{11}\)

\(x-10\left(\dfrac{2}{11.13}+\dfrac{2}{13.15}+\dfrac{2}{15.17}+...+\dfrac{2}{53.55}\right)=\dfrac{3}{11}\)

\(x-10\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{17}+...+\dfrac{1}{53}-\dfrac{1}{55}\right)=\dfrac{3}{11}\)

\(x-10\left(\dfrac{1}{11}-\dfrac{1}{55}\right)=\dfrac{3}{11}\)

\(x-10.\dfrac{4}{55}=\dfrac{3}{11}\)

\(x-\dfrac{8}{11}=\dfrac{3}{11}\)

\(x=\dfrac{3}{11}+\dfrac{8}{11}=1\)

d) Ta có: \(x+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{41\cdot45}=\dfrac{-37}{45}\)

\(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{41}-\dfrac{1}{45}=\dfrac{-37}{45}\)

\(\Leftrightarrow x+\dfrac{1}{5}-\dfrac{1}{45}=\dfrac{-37}{45}\)

\(\Leftrightarrow x=\dfrac{-37}{45}+\dfrac{1}{45}-\dfrac{1}{5}=\dfrac{-36}{45}-\dfrac{1}{5}=\dfrac{-4}{5}-\dfrac{1}{5}=-1\)

Vậy: x=-1

5 tháng 8 2018

a, (x + 1) + (x + 4) + ... + (x + 28) = 155

x + 1 + x + 4 + ... + x + 28 = 155

(x + x + x + ... + x) + (1 + 4 + ... + 28) = 155

x . 10 + 145 = 155

x . 10 = 155 - 145

x . 10 = 10

x = 10 : 10

x = 1

11 tháng 3 2022

a, \(\left(\dfrac{7}{2}-2x\right).\dfrac{10}{3}=\dfrac{22}{3}\Leftrightarrow\dfrac{7}{2}-2x=\dfrac{22}{10}=\dfrac{11}{5}\)

\(\Leftrightarrow2x=\dfrac{13}{10}\Leftrightarrow x=\dfrac{13}{20}\)

b, \(\dfrac{4x}{9}=\dfrac{9}{8}-\dfrac{125}{1000}=1\Leftrightarrow x=\dfrac{9}{4}\)

c, \(-\dfrac{x}{21}=\dfrac{60}{21}\Rightarrow x=-60\)