Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\left(1-\frac{1}{3}\right)\)\(x\left(1-\frac{1}{6}\right)\)\(x\)\(\left(1-\frac{1}{10}\right)\)\(x\)\(\left(1-\frac{1}{15}\right)\)\(x\)\(\left(1-\frac{1}{21}\right)\)\(x\)\(\left(1-\frac{1}{28}\right)\)\(=\)\(\left(\frac{3}{3}-\frac{1}{3}\right)\)\(x\)\(\left(\frac{6}{6}-\frac{1}{6}\right)\)\(x\)\(\left(\frac{10}{10}-\frac{1}{10}\right)\)\(x\)\(\left(\frac{15}{15}-\frac{1}{15}\right)\)\(x\)\(\left(\frac{21}{21}-\frac{1}{21}\right)\)\(x\)\(\left(\frac{28}{28}-\frac{1}{28}\right)\)\(=\)\(\frac{2}{3}x\frac{5}{6}x\frac{9}{10}x\frac{14}{15}x\frac{20}{21}x\frac{27}{28}\)\(=\)\(\frac{2x5x9x14x20x27}{3x6x10x15x21x28}\)\(=\)\(\frac{2x5\left(3x3\right)x\left(2x7\right)x\left(5x4\right)x\left(3x3x3\right)}{3x\left(3x2\right)x\left(5x2\right)x\left(5x3\right)x\left(7x3\right)x\left(4x7\right)}\)\(=\)\(\frac{3}{7}\)
2/
a) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)
\(=\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{17}-\frac{1}{21}\right)\)
\(=1-\frac{1}{21}=\frac{20}{21}\)
b) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot..\cdot\frac{2016}{2017}\)
\(=\frac{1}{2017}\)
c) \(A=2000-5-5-5-..-5\)(có 200 số 5)
\(A=2000-\left(5\cdot200\right)\)
\(A=2000-1000\)
\(A=1000\)
\(\Leftrightarrow10\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{x\times\left(x+1\right)}\right)=9\)
\(\Leftrightarrow\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right)=9\div10\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Leftrightarrow\frac{1}{x+1}=1-\frac{9}{10}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{10}\)
\(\Rightarrow x+1=10\)
\(\Leftrightarrow x=9\)
Vậy x = 9
1/2 . 1/3 . 1/4 . 1/5 . 1/6 . ( x - 1,010 ) = 1/360 - 1/720
1/2 . 1/3 . 1/4 . 1/5 . 1/6 . ( x - 1,010) = 1/720
( x - 1,010 ) . 1/2 . 1/3 . 1/4 . 1/5 . 1/6 = 1/720
( x - 1,010 ) . 1/720 = 1/720
x - 1,010 = 1/720 : 1/720
x - 1,010 = 1
x = 1 + 1,010
x = 2,01
\(\left(x-\frac{1}{2}\right).\frac{5}{2}+\frac{1}{2}=\frac{7}{4}\)
\(\left(x-\frac{1}{2}\right).\frac{5}{2}=\frac{7}{4}-\frac{1}{2}\)
\(\left(x-\frac{1}{2}\right).\frac{5}{2}=\frac{7}{4}-\frac{2}{4}\)
\(\left(x-\frac{1}{2}\right).\frac{5}{2}=\frac{5}{4}\)
\(\left(x-\frac{1}{2}\right)=\frac{5}{4}:\frac{5}{2}\)
\(x-\frac{1}{2}=\frac{1}{2}\)
\(x=\frac{1}{2}+\frac{1}{2}\)
\(x=1\)
a) 15 + 3 ( x - 1 ) = 36
3 ( x - 1 ) = 36 - 15
3 ( x - 1 ) = 21
x - 1 = 21 : 3
x - 1 = 7
x = 7+1
x = 8
Ta co \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+....+\frac{2}{x\cdot\left(x+1\right)}\)
\(\Rightarrow\)\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\cdot\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\)\(2\cdot\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+....+\frac{1}{x\cdot\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Rightarrow\)\(2\cdot\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+...+\frac{1}{x\cdot\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Rightarrow\)\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow x+1=18\)
\(x=17\)
1/2`2+1/3`2+1/4`2+...+1/n`2<1