\(\frac{A}{B}\)biết

\(A=\frac{1}{2\times32}+\frac{1}{3\ti...">

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9 tháng 8 2019

\(taco:A=\frac{1}{2\cdot32}+\frac{1}{3\cdot33}+\frac{1}{4\cdot34}+...+\frac{1}{1988\cdot2018}\)

\(A=\frac{1}{2}-\frac{1}{32}+\frac{1}{3}-\frac{1}{33}+\frac{1}{4}-\frac{1}{34}+...+\frac{1}{1988}-\frac{1}{2018}\)

\(A=\frac{1}{2}-\frac{1}{2018}\)

\(A=\frac{504}{1009}\)

\(B=\frac{1}{2\cdot1989}+\frac{1}{3\cdot1990}+\frac{1}{4\cdot1991}+...+\frac{1}{31\cdot2018}\)

\(B=\frac{1}{2}-\frac{1}{1989}+\frac{1}{3}-\frac{1}{1990}+\frac{1}{4}-\frac{1}{1991}+...+\frac{1}{31}-\frac{1}{2018}\)

\(B=\frac{1}{2}-\frac{1}{1018}\)

\(B=\frac{504}{1009}\)

tu do \(=>\frac{504}{\frac{1009}{\frac{504}{1009}}}< =>1\)

 chuc ban hoc tot nhe >.<

1 tháng 9 2020

a) Ta có : \(\frac{-3}{100}< 0< \frac{2}{3}\)

\(\Rightarrow\frac{-3}{100}< \frac{2}{3}\)

b) Ta có : \(\frac{267}{268}< 1< \frac{1347}{1343}\)

\(\Rightarrow\frac{267}{268}< \frac{1347}{1343}\)

\(\Rightarrow\frac{267}{-268}< \frac{-1347}{1343}\)

c) Ta có : \(\frac{2017.2018-1}{2017.2018}=\frac{2017.2018}{2017.2018}-\frac{1}{2017.2018}=1-\frac{1}{2017.2018}\)

                 \(\frac{2018.2019-1}{2018.2019}=\frac{2018.2019}{2018.2019}-\frac{1}{2018.2019}=1-\frac{1}{2018.2019}\)

mà \(2017.2018< 2018.2019\)

\(\Rightarrow\frac{1}{2017.2018}>\frac{1}{2018.2019}\)

\(\Rightarrow1-\frac{1}{2017.2018}< 1-\frac{1}{2018.2019}\)

\(\Rightarrow\frac{2017.2018-1}{2017.2018}< \frac{2018.2019-1}{2018.2019}\)

d) Ta có : \(\frac{2017.2018}{2017.2018+1}=\frac{2017.2018+1}{2017.2018+1}-\frac{1}{2017.2018+1}=1-\frac{1}{2017.2018+1}\)

                 \(\frac{2018.2019}{2018.2019+1}=\frac{2018.2019+1}{2018.2019+1}-\frac{1}{2018.2019+1}=1-\frac{1}{2018.2019+1}\)

mà \(2017.2018+1< 2018.2019+1\)

\(\Rightarrow\frac{1}{2017.2018+1}>\frac{1}{2018.2019+1}\)

\(\Rightarrow1-\frac{1}{2017.2018+1}< 1-\frac{1}{2018.2019+1}\)

\(\Rightarrow\frac{2017.2018}{2017.2018+1}< \frac{2018.2019}{2018.2019+1}\)

 

9 tháng 3 2020

\(B=\frac{1}{1.2}=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)

\(B=\left(1-\frac{1}{2018}\right)-\left(\frac{1}{2}-\frac{1}{2}\right)-...-\left(\frac{1}{2017}-\frac{1}{2017}\right)\)

\(B=1-\frac{1}{2018}=\frac{2017}{2018}\)

Vậy \(B=\frac{2017}{2018}\)

6 tháng 7 2018

a/\(\left(2-x\right)\times-3=\left(3x-1\right)\times4\)4

\(\Rightarrow-6+3x=12x-4\)

\(\Rightarrow-2=9x\)

\(\Rightarrow x=\frac{-2}{9}\)

bài b cx tương tự nha

ta có;\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}=\frac{a+b}{c+d}\)(THEO TÍNH CHẤT DÃY TỈ SỐ BẰNG NHAU)

\(\Rightarrowđpcm\)

12 tháng 6 2018

1. a) \(\frac{3}{4}-\frac{-1}{2}+\frac{1}{3}=\frac{3}{4}+\frac{1}{2}+\frac{1}{3}=\frac{9}{12}+\frac{6}{12}+\frac{4}{12}=\frac{19}{12}\)

   b) \(5\frac{5}{27}+\frac{7}{23}+\frac{1}{2}-\frac{5}{27}+\frac{16}{23}\)

\(=\frac{140}{27}-\frac{5}{27}+\frac{7}{23}+\frac{16}{23}+\frac{1}{2}\)

\(=\frac{135}{27}+\frac{23}{23}+\frac{1}{2}\)

\(=5+1+0,5=6,5\)

2) a) 1/2 + 2/3x = 1/4

=> 2/3x            = 1/4 - 1/2

=> 2/3x            = -1/4

=> x                = -1/4 : 2/3

=> x                = -3/8

b) 3/5 + 2/5 : x = 3 1/2

=> 3/5 + 2/5 : x = 7/2

=>         2/5 : x  = 7/2 - 3/5

=>         2/5 : x  = 29/10

=>               x    = 2/5 : 29/10

=>               x    = 4/29

c) x+4/2004 + x+3/2005 = x+2/2006 + x+1/2007

=> x+4/2004 + 1 + x+3/2005 + 1 = x+2/2006 + 1 + x+1/2007 + 1

=>   x+2008/2004 + x+2008/2005 = x+2008/2006 + x+2008/2007

=>  x+2008/2004 + x+2008/2005 - x+2008/2006 - x+2008/2007 = 0

=> (x+2008). (1/2004 + 1/2005 - 1/2006 - 1/2007) = 0

Vì 1/2004 + 1/2005 - 1/2006 - 1/2007 khác 0

Nên x + 2008 = 0 <=> x = -2008

Vậy x = -2008

12 tháng 6 2018

1,a,\(\frac{3}{4}-\frac{-1}{2}+\frac{1}{3}=\frac{3}{4}+\frac{2}{4}+\frac{1}{3}=\frac{5}{4}+\frac{1}{3}=\frac{15}{12}+\frac{4}{12}=\frac{19}{12}\)

  b, \(5\frac{5}{27}+\frac{7}{23}+\frac{1}{2}-\frac{5}{27}+\frac{16}{23}=\frac{140}{27}-\frac{5}{27}+\frac{7}{23}+\frac{16}{23}+\frac{1}{2}=\frac{135}{27}+\frac{23}{23}+\frac{1}{2}=5+1+\frac{1}{2}=\frac{13}{2}\)2,a,\(\frac{1}{2}+\frac{2}{3}.x=\frac{1}{4}\)

    <=>\(\frac{2}{3}.x=-\frac{1}{2}\)

   <=>\(x=-\frac{3}{4}\)

b,\(\frac{3}{5}+\frac{2}{5}\div x=3\frac{1}{2}\)

 <=>\(\frac{2}{5x}=\frac{29}{10}\)

 <=>\(x=\frac{29}{4}\)

c,\(\frac{x+4}{2004}+\frac{x+3}{2005}=\frac{x+2}{2006}+\frac{x+1}{2007}\)

<=> \(\frac{x+4}{2004}+1+\frac{x+3}{2005}+1=\frac{x+2}{2006}+1+\frac{x+1}{2007}+1\)

<=>\(\frac{x+2008}{2004}+\frac{x+2008}{2005}=\frac{x+2008}{2006}+\frac{x+2008}{2007}\)

<=>\(\left(x+2008\right)\left(\frac{1}{2004}+\frac{1}{2005}-\frac{1}{2006}-\frac{1}{2007}\right)\)=0

<=>x+2008=0 vì cái ngoặc còn lại\(\ne0\)

<=>x=-2008

 Vậy x=-2008

Bạn nhớ tk cho mình vì mình đã chăm chỉ làm hết bài bạn hỏi nha!

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