1/3+1/6+1/10+...+2/[x.(x+1)]=4020/2011
nhớ trình bày cách làm nghen
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
25 tháng 4 2022
1) 1/3 x 1/2 x 3/7 = 3/42 = 1/14
2) 5/4 x 1/3 +1/7 = 5/12 + 1/7 = 35/84 + 12/84 = 47/84
3) 8 x ( 8/9 - 2/3 ) = 8 x 2/9 = 16/9
4) 5/6 x 48/20 x 1/2 = 240/240 = 1
5) ( 2/5 + 3/4 ) + 8 = 23/20 + 8 = 23//20 + 160/20 = 183/20
6) 10 x ( 1/2 - 1/5 ) = 10 x 3/10 = 10/1 x 3/10 = 30/10 = 3
30 tháng 6 2023
1: \(=\dfrac{1}{3}\cdot\dfrac{3}{7}\cdot\dfrac{1}{2}=\dfrac{1}{7\cdot2}=\dfrac{1}{14}\)
2: =5/12+1/7
=35/84+12/84=47/84
3: =8(8/9-6/9)
=8*2/9=16/9
4: \(=\dfrac{5}{12}\cdot\dfrac{12}{5}=1\)
5: =16/5+6
=16/5+30/5=46/5
6: =10*1/2-10*1/5
=5-2=3
TM
13 tháng 7 2017
a)\(\frac{5}{6}+\frac{3}{4}x=3\Leftrightarrow\frac{3}{4}x=\frac{13}{6}\Leftrightarrow x=\frac{26}{9}\)
b)\(\frac{8}{x}\cdot\frac{3}{4}=\frac{9}{10}\Leftrightarrow\frac{8}{x}=\frac{6}{5}\Leftrightarrow x=\frac{8\cdot5}{6}=\frac{20}{3}\)
c)\(3\cdot\left(x+\frac{1}{2}\right)-\frac{1}{3}=\frac{2}{5}\Leftrightarrow3\left(x+\frac{1}{2}\right)=\frac{11}{15}\Leftrightarrow x+\frac{1}{2}=\frac{11}{45}\Leftrightarrow x=-\frac{23}{90}\)
d)\(\frac{1}{4}+\frac{x}{3}=\frac{5}{6}\Leftrightarrow\frac{x}{3}=\frac{7}{12}\Leftrightarrow x=\frac{7\cdot3}{12}=\frac{7}{4}\)
14 tháng 7 2017
Bạn ơi , cái dấu hai chiều là sao ? trả lời nhanh cho mình nhé !
HM
0
KA
11 tháng 9 2017
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{x.\left(x+1\right)}=1\)
\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=1\)
\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=1\)
PT
0
20 tháng 4 2016
nhân cả 2 vế của đẳng thức với 1/2 ta được
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.....+\frac{1}{x\left(x+1\right)}=\frac{2014}{2015}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{x\left(x+1\right)}=\frac{2014}{2015}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-......+\frac{1}{x}-\frac{1}{x+1}=\frac{2014}{2015}\)
\(=\frac{1}{2}-\frac{1}{x+1}=\frac{2014}{2015}\)
\(=>\frac{1}{x+1}=\frac{1}{2}-\frac{2014}{2015}\)
\(\frac{1}{x+1}=-\frac{2013}{4030}\)
hay \(1:\left(x+1\right)=-\frac{2013}{4030}\)
\(x+1=-\frac{4030}{2013}\)
\(=>x=-\frac{6043}{2013}\)
TH
30 tháng 8 2018
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4020}{2011}\)
\(\Rightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4020}{2011}\)
\(\Rightarrow\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4020}{2011}\)
\(\Rightarrow2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{4020}{2011}\)
\(\Rightarrow\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{4020}{2011}:2\)
\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2010}{2011}\)
\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{2010}{2011}\)
\(\Rightarrow\dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{2010}{2011}\)
\(\Rightarrow\dfrac{1}{x+1}=-\dfrac{2009}{4022}\)
\(\Rightarrow4022=-2009\left(x+1\right)\)
\(\Rightarrow4022=-2009x-2009\)
\(\Rightarrow2009x=-2009-4022\)
\(\Rightarrow2009x=-6031\)
\(\Rightarrow x=-\dfrac{6031}{2009}\)
1/3+1/6+1/10+...+2/[x.(x+1)]= 2011/2013
12(13+16+...1x(x+1)=2011201312(13+16+...1x(x+1)=20112013
12.3+13.4+14.5+...+1x(x+1)=2011201312.3+13.4+14.5+...+1x(x+1)=20112013
12−13+13−14+...+1x−1x+1=2011201312−13+13−14+...+1x−1x+1=20112013
12−1x+1=2011201312−1x+1=20112013
1x+1=12−201120131x+1=12−20112013
1x+1=−200940261x+1=−20094026
(x+1).−2009=4026(x+1).−2009=4026
−2009x+(−2009)=4026−2009x+(−2009)=4026
−2009x=4026−(−2009)−2009x=4026−(−2009)
−2009x=6035−2009x=6035
x=−60352009