\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+.......+\frac{1}{nx\left(n+1\right)}=\frac{49}{100}\)
n bằng...,........
ai đúng mk tick
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{120x121}+\frac{1}{121x122}\)
Mk bó tay òi, ai lm đc hông
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{120x121}+\frac{1}{121x122}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{120}-\frac{1}{121}+\frac{1}{121}-\frac{1}{122}\)
Ta thấy nếu + 1/3 và đồng thời - 1/3 thì đc số ban đầu nên áp dụng quy luật "trái dấu ta gạch"
\(=\)\(\frac{1}{2}-\frac{1}{122}\)
\(=\frac{30}{61}\)
P/s: Cái dòng chữ Ta thấy... bn đừng viết dzô nha, cái đó mk giải thích thêm thui cho bn hỉu
Mk lm mãi mới đc đó. Bài này ko khó cũng ko dễ chỉ thuộc loại bt thui nha
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{120x121}+\frac{1}{121x122}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{120}-\frac{1}{121}+\frac{1}{121}-\frac{1}{122}\)
\(=\frac{1}{2}-\frac{1}{122}\)
\(=\frac{61}{122}-\frac{1}{122}\)
\(=\frac{60}{122}=\frac{30}{61}\)
Ủng hộ mk nha ^_-
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{121.122}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+......+\frac{1}{121}-\frac{1}{122}\)
\(=\frac{1}{2}-\frac{1}{122}\)
\(=\frac{30}{61}\)
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
Ta có: 1/1x2 + 1/2x3 + 1/3x4 +...+ 1/X 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
=> 1/(X + 1) = 1 - 499/500
=> 1/(X + 1) = 1/500
=> X + 1 = 500
=> X = 500 - 1
=> X = 499
Đáp số: X = 499
\(\frac{1}{2x3}x\frac{1}{3x4}x\frac{1}{4x5}x............x\frac{1}{98x99}x\frac{1}{99x100}\)
Hãy tính nhanh ,ai nhanh mình tick cho
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow\frac{1}{2}-0+0+...+0-\frac{1}{100}\)
\(\Rightarrow\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)
Tính bằng cách thuận tiện :
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{99x100}\)
Mình sẽ tick cho một bạn nhanh nhất ! ^_^
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)
Đặt \(M=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(M=1-\frac{1}{100}\)
\(M=\frac{99}{100}\)
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+....+\frac{1}{99\times100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Tìm số tự nhiên a biết : \(\frac{1}{2x3}\)+ \(\frac{1}{3x4}\)+ \(\frac{1}{4x5}\)+......+\(\frac{1}{ax\left(a+1\right)}\)=\(\frac{49}{100}\)
Trả lời a = ....................
\(\frac{1}{2\times3}+\frac{1}{3\times4}+............+\frac{1}{a\times\left(a+1\right)}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..............+\frac{1}{a}-\frac{1}{a+1}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{a+1}=\frac{49}{100}\)
\(\Rightarrow\frac{1}{a+1}=\frac{1}{2}-\frac{49}{100}\)
\(\Rightarrow\frac{1}{a+1}=\frac{1}{100}\)
\(\Rightarrow a+1=100\)
\(\Rightarrow a=99\)
Đáp số là a = 99 nha còn cách làm thì Nguyễn Hung Phat đã làm rồi nha
T ik nha bạn =))
Chúc bạn học tốt nhé !!!
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, 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:
\(\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+....+\frac{1}{8x9}+\frac{1}{9x10}\right)x100-\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]:\frac{1}{2}=89\)