\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).....\left(\frac{1}{100}-1\right)\)

\(=\frac{3}{4}.\frac{8}{9}.....\frac{99}{100}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.....\frac{9.11}{10.10}\)

\(=\frac{\left(1.3\right).\left(2.4\right).....\left(9.11\right)}{\left(2.2\right).\left(3.3\right).....\left(10.10\right)}\)

\(=\frac{\left(1.2.3.....9\right).\left(3.4.5.....11\right)}{\left(2.3.4.....10\right).\left(2.3.4.....10\right)}\)

\(=\frac{1.11}{10.2}=\frac{11}{20}\)

\(S=\frac{3}{4}-0,25-\left[\frac{7}{3}+\left(\frac{-9}{2}\right)\right]-\frac{5}{6}\)

\(\Rightarrow S=\frac{3}{4}-\frac{1}{4}-\left(\frac{7}{3}-\frac{9}{2}\right)-\frac{5}{6}\)

\(\Rightarrow S=\frac{1}{2}-\frac{7}{3}+\frac{9}{2}-\frac{5}{6}\)

\(\Rightarrow S=\frac{3}{6}-\frac{14}{6}+\frac{27}{6}-\frac{5}{6}\)

\(\Rightarrow S=\frac{11}{6}\)

đây bạn nhé 

đây nhé bạn 

Vì mm' // nn' ( bài cho )

=> \(\widehat{mMd'}+\widehat{dNn}=180^o\)( do là 2 góc so le trong )

Mà \(\widehat{mMd'}=2\widehat{dNn}\)

=> \(2\widehat{dNn}+\widehat{dNn}=180^o\)

=> \(3\widehat{dNn}=180^o\)

=> \(\widehat{dNn}=60^o\Leftrightarrow\widehat{mMd'}=120^o\)

Ta có : \(\widehat{dNn}=\widehat{mMd}\)( do là 2 góc đồng vị )

=> \(\widehat{mMd}=60^o\)

Lại có : \(\widehat{mMd'}=\widehat{dNn'}\)( do là 2 góc so le trong 

=> \(\widehat{dNn'}=120^o\)

Ta có :

\(x-3y=\frac{1}{2}=0,5\)

\(\frac{x}{y}=\frac{1}{3}\Rightarrow\frac{x}{1}=\frac{y}{3}\)

Áp dụng tính chất dãy tỉ số bằng nhau , ta có :

\(\frac{x}{1}=\frac{y}{3}=\frac{3y}{9}=\frac{x-3y}{1-9}=\frac{0,5}{-8}=\frac{-1}{16}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{-1}{16}.1=\frac{-1}{16}\\y=\frac{-1}{16}.9:3=\frac{-3}{16}\end{cases}}\)

\(-1+\frac{1}{3}-\frac{1}{9}-\frac{1}{81}\)

\(=\frac{-81}{81}+\frac{27}{81}-\frac{9}{81}-\frac{1}{81}\)

\(=\frac{-64}{81}\)

cảm ơn bạn nha