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\(a,\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}=\frac{1}{3}\)
\(b,\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\)
\(=\frac{1\times2\times3}{2\times3\times4}=\frac{1}{4}\)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{100}\right).200x=4036\)
\(\Leftrightarrow\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{99}{100}.200x=4036\)
\(\Leftrightarrow\frac{1.2.3...99}{2.3.4....100}.200x=4036\)
\(\Leftrightarrow\frac{1}{100}.200x=4036\)
\(\Leftrightarrow\frac{1}{100}.200x=4036\)
\(\Leftrightarrow2x=4036\)
\(\Leftrightarrow x=4036:2=2018\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{100}\right)\times200\times x=4036\)
=> \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{99}{100}\times200\times x=4036\)
=> \(\frac{1\times2\times...\times99}{2\times3\times...\times100}\times200\times x=4036\)
\(\Rightarrow\frac{1}{100}\times200\times x=4036\)
\(\Rightarrow2\times x=4036\)
=> x = 2018
\(\frac{4}{5}+\left(x:\frac{2}{3}-\frac{1}{2}\right)=\frac{9}{10}\)
\(x:\frac{2}{3}-\frac{1}{2}=\frac{9}{10}-\frac{4}{5}\)
\(x:\frac{2}{3}-\frac{1}{2}=\frac{1}{10}\)
\(x:\frac{2}{3}=\frac{1}{10}-\frac{1}{2}\)
\(x:\frac{2}{3}=\frac{-2}{5}\)
\(x=\frac{-2}{5}X\frac{2}{3}\)
\(x=\frac{-4}{15}\)
\(\frac{4}{5}+\left(x:\frac{2}{3}-\frac{1}{2}\right)=\frac{9}{10}\)
\(x:\frac{2}{3}-\frac{1}{2}=\frac{1}{10}\)
\(x:\frac{2}{3}=\frac{3}{5}\)
\(x=\frac{2}{5}\)
\(\left(2.8x-32\right):\frac{2}{3}=90\)
\(2.8\cdot x-32=90\cdot\frac{2}{3}\)
\(\frac{14}{5}x-32=60\)
\(\frac{14}{5}x=60+32\)
\(\frac{14}{5}x=92\)
\(x=\frac{230}{7}\)
B , c , d tương tự
[ 19/20 x 3/4 + 1/20 x 3/4 ] x [ 1/2 x 3/4 -2/4 x 3/4 ]
=[ 3/4 x [19/20 + 1/20 ] x [3/4 x [2/4 - 1/2]
=[ 3/4 x 1 ] x [3/4 x 0 ]
=0
\(\left(\frac{19}{20}.\frac{3}{4}+\frac{1}{20}.\frac{3}{4}\right).\left(\frac{1}{2}.\frac{3}{4}-\frac{2}{4}.\frac{3}{4}\right)\)
\(=\left(\frac{19}{20}.\frac{3}{4}+\frac{1}{20}.\frac{3}{4}\right).\left(\frac{1}{2}.\frac{3}{4}-\frac{1}{2}.\frac{3}{4}\right)\)
\(=\left(\frac{19}{20}.\frac{3}{4}+\frac{1}{20}.\frac{3}{4}\right).0\)
\(=0\)