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\(X-\frac{2}{3}=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}\)

\(=>X-\frac{2}{3}=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(=>X-\frac{2}{3}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(=>X-\frac{2}{3}=1-\frac{1}{100}\)

\(=>X-\frac{2}{3}=\frac{100}{100}-\frac{1}{100}\)

\(=>X-\frac{2}{3}=\frac{99}{100}\)

\(=>X=\frac{99}{100}+\frac{2}{3}\)

\(=>X=\frac{497}{300}\)

Lưu ý: dấu chấm thay dấu nhân

7 tháng 8 2015

\(x-\frac{2}{3}=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}\)

Tổng vế phải gồm : \(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}\)

 \(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{98}-\frac{1}{99}\right)+\left(\frac{1}{99}-\frac{1}{100}\right)\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{100}{100}-\frac{1}{100}\)

\(=\frac{99}{100}\)

Với vế trái, ta có : \(x-\frac{2}{3}=\frac{99}{100}\)

\(x-\frac{2}{3}=\frac{99}{100}\)

\(x=\frac{99}{100}+\frac{2}{3}\)

\(x=\frac{497}{300}\)

11 tháng 3 2016

T là 99/100 . Đúng 100% luôn nhé .

10 tháng 4 2018

a) \(\frac{1,11+0,19-12,2}{0,296+0,094}-x=\left(\frac{1}{2}+\frac{1}{3}\right):2\)

Đề đúng:

\(\frac{1,11+0,19-1,3.2^6}{0,296+0,094}-x=\left(\frac{1}{2}+\frac{1}{3}\right):2\)

\(\frac{1,3-1,3.64}{0,39}-x=\left(\frac{3}{6}+\frac{2}{6}\right).\frac{1}{2}\)

\(\frac{1,3.\left(-63\right)}{0,39}-x=\frac{5}{6}.\frac{1}{2}\)

\(\frac{-81,9}{0,39}-x=\frac{5}{12}\)

\(\left(-210\right)-x=\frac{5}{12}\)

\(x=\left(-210\right)-\frac{5}{12}\)

\(x=\frac{-2520}{12}-\frac{5}{12}\)

\(x=\frac{-2525}{12}\)

b) \(x:\left(3\frac{1}{2}-5\frac{1}{6}\right)=4\frac{1}{5}-6\frac{2}{3}\)

\(x:\left(\frac{7}{2}-\frac{31}{6}\right)=\frac{21}{5}-\frac{20}{3}\)

\(x:\left(\frac{21}{6}-\frac{31}{6}\right)=\frac{63}{15}-\frac{100}{15}\)

\(x:\frac{-10}{6}=\frac{-37}{15}\)

\(x.\frac{6}{-10}=\frac{-37}{5}\)

\(x.\frac{-6}{10}=\frac{-37}{5}\)

\(x.\frac{-3}{5}=\frac{-37}{5}\)

\(x=\frac{-37}{5}:\frac{-3}{5}\)

\(x=\frac{-37}{5}.\frac{5}{-3}\)

\(x=\frac{-37}{-3}\)

\(x=\frac{37}{3}\)

10 tháng 4 2018

Sai đề bài

Lẽ ra câu a chỉ chia 2 thì chia 22

Sai đề bài mina-san 

25 tháng 6 2017

Ta có : \(\frac{1}{4}+\frac{1}{3}:\frac{1}{x}=\frac{11}{12}\)

\(\Rightarrow\frac{1}{3}:\frac{1}{x}=\frac{11}{12}-\frac{1}{4}\)

\(\frac{1}{3}:\frac{1}{x}=\frac{2}{3}\)

\(\frac{1}{x}=\frac{1}{3}:\frac{2}{3}\)

\(\frac{1}{x}=\frac{1}{3}\times\frac{3}{2}\)

\(\frac{1}{x}=\frac{1}{2}\)

=> x = 2

25 tháng 6 2017

a) \(\frac{x\div3-16}{2}+21=38\)

\(\frac{x\div3-16}{2}=38+21\)

\(\frac{x\div3-16}{2}=59\)

\(x\div3-16=59.2\)

\(x\div3-16=118\)

\(x\div3=118+16\)

\(x\div3=134\)

\(x=134.3\)

\(x=402\)

b) \(\frac{1}{4}+\frac{1}{3}\div\frac{1}{x}=\frac{11}{12}\)

\(\frac{1}{3}\div\frac{1}{x}=\frac{11}{12}-\frac{1}{4}\)

\(\frac{1}{3}\div\frac{1}{x}=\frac{2}{3}\)

\(\frac{1}{x}=\frac{1}{3}\div\frac{2}{3}\)

\(\frac{1}{x}=\frac{1}{2}\)

Vậy x = ....

3 tháng 7 2018

Câu b:

\(\frac{21}{8}:\frac{5}{6}+\frac{1}{2}:\frac{5}{6}\)

\(\frac{63}{20}+\frac{3}{5}\)

\(\frac{15}{4}\)

7 tháng 7 2018

\(\left(\frac{21}{8}+\frac{1}{2}\right):\frac{5}{6}\)

\(\frac{25}{8}:\frac{5}{6}\)

\(\frac{25}{8}.\frac{6}{5}\)

\(\frac{30}{8}\)

14 tháng 7 2015

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

18 tháng 4 2015

Ta có \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)
                                              \(\frac{15}{16}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}\)
                                              \(\frac{15}{16}:x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\)
                                              \(\frac{15}{16}:x=1-\frac{1}{12}\)
                                              \(\frac{15}{16}:x=\frac{11}{12}\)
                                              \(x=\frac{15}{16}:\frac{11}{12}\)
                                              \(x=\frac{180}{176}\)
Đúng thì like nha

5 tháng 9 2015

\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+....+\frac{1}{32}\)

\(\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right):x=\frac{1}{1\times2}+\frac{1}{2\times3}+.....+\frac{1}{11\times12}\)

\(\frac{15}{16}:x=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{12}\)

\(\frac{15}{16}:x=1-\frac{1}{12}\)

\(\frac{15}{16}:x=\frac{11}{12}\)

\(x=\frac{15}{16}:\frac{11}{12}\)

\(x=\frac{45}{44}\)

5 tháng 9 2015

Tính \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)

2 x A = \(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)

2 x A - A = A =  \(1-\frac{1}{16}=\frac{15}{16}\)

Tính \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+....+\frac{1}{11\times12}\)

 \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}=\frac{1}{1}-\frac{1}{12}=\frac{11}{12}\)

Ta có: \(\frac{15}{16}:x=\frac{11}{12}\Rightarrow x=\frac{15}{16}:\frac{11}{12}=\frac{15}{16}\times\frac{12}{11}=\frac{45}{44}\)

Vậy...