Tìm \(X\), biết :
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.....+\frac{1}{Xx\left(x+1\right)}=\frac{499}{500}\)
Ai giúp mk cho 5 tick
Tìm x, biết:
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+........+\frac{1}{Xx\left(x+1\right)}=\frac{499}{500}\)
Ai đúng cho 3tick
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{499}{500}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{499}{500}\)
\(1-\frac{1}{x+1}=\frac{499}{500}\)
\(\frac{1}{x+1}=1-\frac{499}{500}=\frac{1}{500}\)
=> x + 1 = 500
=> x = 500 - 1
=> x = 499
Vậy x = 499
1/1.2 + 1/2.3 + 1/3.4 +...+ 1/x.(x+1)=499/500
1 - 1/2 + 1/2 -1/3 + 1/3 - 1/4 +...+ 1/x -1/(x+1) =499/500
1-1/(x+1)=499/500
=>x/(x+1)=499/500
=>x=499
Tính nhanh
\(G=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
Tìm x
\(\frac{3}{1x2}+\frac{3}{2x3}+\frac{3}{3x4}+.....+\frac{3}{Xx\left(X+1\right)}=\frac{6042}{2015}\)
Ai nhanh mk sẽ tick
\(G=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(G=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^5}\)
\(3G=3+1+\frac{1}{3}+...+\frac{1}{3^4}\)
\(3G-G=\left(3+1+...+\frac{1}{3^4}\right)-\left(1+\frac{1}{3}+...+\frac{1}{3^5}\right)\)
\(2G=3-\frac{1}{3^5}\)
\(2G=3-\frac{1}{243}\)
\(2G=\frac{729}{243}-\frac{1}{243}\)
\(G=\frac{728}{243}:2\)
\(G=\frac{364}{243}\)
\(\frac{3}{1.2}+\frac{3}{2.3}+...+\frac{3}{x.\left(x+1\right)}=\frac{6042}{2015}\)
\(3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{6042}{2015}\)
\(1-\frac{1}{x+1}=\frac{6042}{2015}:3\)
\(1-\frac{1}{x-1}=\frac{2014}{2015}\)
\(\frac{1}{x-1}=1-\frac{2014}{2015}\)
\(\frac{1}{x-1}=\frac{1}{2015}\)
\(\Rightarrow x-1=2015\)
\(\Rightarrow x=2016\)
Tìm x trong biểu thức sau:
\(\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+....+\frac{1}{8x9}+\frac{1}{9x10}\right)x100-\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]:\frac{1}{2}=89\)
các bn giúp mk nha
\(\frac{1}{2x3}+\frac{1}{3x4}+......+\frac{1}{Xx\left(Xx1\right)}=\frac{24}{50}\)ai nhah mk sẽ tik
\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}\)\(=\frac{24}{50}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x.1}\)=\(\frac{24}{50}\)
=\(\frac{1}{2}-\frac{1}{x.1}=\frac{24}{50}\)
=\(\frac{1}{x.1}=\frac{1}{2}-\frac{24}{50}\)
=\(\frac{1}{x.1}=\frac{1}{50}\)
\(\Rightarrow\)\(x.1=50\)
\(\Rightarrow x=50\)
Tìm X ( x này là nhân )
\(\frac{1}{1x2}+\frac{1}{2x3}+.....+\frac{1}{Xx\left(x+1\right)}=\frac{9}{10}\)
Sửa đề:
\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{x\times\left(x+1\right)}=\frac{9}{10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(1-\frac{1}{x}=\frac{9}{10}\)
\(\frac{1}{x}=1-\frac{9}{10}=\frac{1}{10}\)
Vậy, x = 10.
Ko bt có right ko?
Nhầm.
Chuyển \(1-\frac{1}{x}\)thành \(1-\frac{1}{x+1}\)
\(1-\frac{1}{x+1}=\frac{9}{10}\)
\(\frac{1}{x+1}=1-\frac{9}{10}=\frac{1}{10}\)
Vậy x = 10 - 1 = 9
Thế ms right chứ!
\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\Leftrightarrow\frac{1}{x+1}=\frac{1}{1}-\frac{9}{10}=\frac{1}{10}\)
\(\Leftrightarrow x+1=10\Rightarrow x=10-1=9\)
Vậy x = 9
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+.......+\frac{1}{nx\left(n+1\right)}=\frac{49}{100}\)
n bằng...,........
ai đúng mk tick
\(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{n\times\left(n+1\right)}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{n+1}=\frac{49}{100}\)
\(\Rightarrow\frac{n+1-2}{2\left(n+1\right)}=\frac{49}{100}\)
\(\Rightarrow\frac{n-1}{2n+2}=\frac{49}{100}\)
\(\Rightarrow100\left(n-1\right)=49\left(2n+2\right)\)
\(\Rightarrow100n-100=98n+98\)
\(\Rightarrow2n=198\)
=> n = 99
Vậy n = 99
\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+....+\(\frac{1}{n}\)-\(\frac{1}{n+1}\)=\(\frac{49}{100}\)
\(\frac{1}{2}\)-\(\frac{1}{n+1}\)=\(\frac{49}{100}\)
\(\frac{1}{n+1}\)=\(\frac{1}{2}\)-\(\frac{49}{100}\)
\(\frac{1}{n+1}\)=\(\frac{1}{100}\)
=> n+1=100
n=100-1
n=99
\(\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{nx\left(n+1\right)}=\frac{49}{100}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{49}{100}\)
\(\frac{1}{2}-\frac{1}{n+1}=\frac{49}{100}\)
\(\frac{1}{n+1}=\frac{1}{2}-\frac{49}{100}\)
\(\frac{1}{n+1}=\frac{1}{100}\)
n + 1 = 100
n = 100 - 1
n = 99
Bn k cho mik nhé!
\(\frac{1}{1x2}+\frac{1}{2x3}+....+\frac{1}{x\left(x+1 \right)}=\frac{2008}{2009}\)tìm x biết
\(\frac{1}{1x2}\)+\(\frac{1}{2x3}\)+\(\frac{1}{3x4}\)+...+\(\frac{1}{yx\left(y+1\right)}\)=\(\frac{996}{997}\)
Ai nhanh mình tick nè !
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{y\times\left(y+1\right)}=\frac{996}{997}\)
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{y}-\frac{1}{y+1}=\frac{996}{997}\)
\(\Leftrightarrow1-\frac{1}{y+1}=\frac{996}{997}\)
\(\Leftrightarrow\frac{1}{y+1}=1-\frac{996}{997}=\frac{1}{997}\)
\(\Leftrightarrow y+1=997\Leftrightarrow y=996\)
Vậy y = 996
1/1×2 + 1/2×3 + 1/3×4 + ... + 1/ y x (y+1) =996/997
1-1/2+1/2-1/3+1/3-1/4+...+1/y - 1/y+1 =996/997
1-1/y+1=996/997
1/ y+1 =1-996/997
1/y+1 = 997/997-996/997
1/y+1=1/997
=> y+1 =997
y=997-1
y=996
Vậy y = 996
a)(864x11-423x4):(432x(3+6+9+...+27-132))
b)1x2+2x3+3x4+...+99x100
ec)\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+\left(1+2+3+4\right)+...+\left(1+2+3+...+99\right)}{1x9+2x98+3x97\: +....+99x1}\)
giúp mk với , mk tick cho , nha !!!!