\(\frac{1}{1.101}\)+ \(\frac{1}{2.102}\)+
K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

4 tháng 5 2017

deex vậy

24 tháng 5 2017

Ta có:

\(\left(\frac{1}{1.101}+\frac{1}{2.102}+\frac{1}{3.103}+...+\frac{10}{10.110}\right)x=\)\(\frac{1}{1.11}+\frac{1}{2.12}+...+\frac{1}{100.110}\)

\(\Rightarrow\left(\frac{100}{1.101}+\frac{100}{2.202}+\frac{100}{3.303}+...+\frac{100}{10.101}\right)x=\)\(10.\left(\frac{10}{1.11}+\frac{10}{2.12}+...+\frac{10}{100.110}\right)\)

\(\Rightarrow\left(1-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\right)x=\)\(10.\left(1-\frac{1}{11}+\frac{1}{2}-\frac{1}{12}+...+\frac{1}{100}-\frac{1}{110}\right)\)

\(\Rightarrow\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{110}\right)\right]x\)\(=\)\(10.\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)-\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{110}\right)\right]\)

\(\Rightarrow\left[ \left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\right]x=\)\(10.\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\right]\)

\(\Rightarrow x=10\)

25 tháng 5 2017

Thiếu Đề !

5 tháng 7 2017

Bài 2: 

a, 1/3 + 1/2 : x = -4

=> 1/2 : x = -4 - 1/3 

=> 1/2 : x = -13/3

=> x = 1/2 ; -13/3

=> x = -3/26

Vậy x = -3 / 26

5 tháng 7 2017

Bài 2: 

b, x2 - 4x = 0

=> x.(x - 4) =0

=> x=0 hoặc x - 4 = 0

x - 4= 0 => x=4

Vậy x=0 và x=4

27 tháng 9 2020

a) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.........+\frac{2}{x\left(x+1\right)}=\frac{1998}{2000}\)

\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.......+\frac{2}{x\left(x+1\right)}=\frac{1998}{2000}\)

\(\Leftrightarrow2.\left[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+......+\frac{1}{x\left(x+1\right)}\right]=\frac{1998}{2000}\)

\(\Leftrightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{x\left(x+1\right)}=\frac{999}{2000}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+......+\frac{1}{x}-\frac{1}{x+1}=\frac{999}{2000}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{999}{2000}\)\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2000}\)

\(\Leftrightarrow x+1=2000\)\(\Leftrightarrow x=1999\)

Vậy \(x=1999\)

b) \(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+......+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)

\(\Leftrightarrow\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.....+\frac{2}{\left(2x+1\right)\left(2x+3\right)}=\frac{15.2}{93}\)

\(\Leftrightarrow\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{2x+1}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\Leftrightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\Leftrightarrow\frac{1}{2x+3}=\frac{1}{93}\)\(\Leftrightarrow2x+3=93\)

\(\Leftrightarrow2x=90\)\(\Leftrightarrow x=45\)

Vậy \(x=45\)

2: =>2x-1/4=5/6-1/2x

=>5/2x=5/6+1/4=13/12

=>x=13/30

3: =>3x-5/6=2/3-1/2x

=>3,5x=2/3+5/6=4/6+5/6=9/6=3,2

hay x=32/35