\(A=\frac{9}{10}\times\frac{10}{11}\times\frac{11}{12}\times...\times\frac{99}{100}\)

\(A=\frac{9\times10\times11\times...99}{10\times11\times12\times...\times100}\)

\(\Rightarrow A=\frac{9}{100}\)

\(A=\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)

\(A=\left(-\frac{9}{10}\right)\cdot\left(-\frac{10}{11}\right)\cdot\left(-\frac{11}{12}\right)\cdot....\cdot\left(-\frac{98}{99}\right)\left(-\frac{99}{100}\right)\)

\(A=\frac{\left(-9\right)\left(-10\right)\left(-11\right)...\left(-98\right)\left(-99\right)}{10\cdot11\cdot12\cdot....\cdot99\cdot100}\)

\(A=\frac{9\cdot10\cdot11\cdot....\cdot98\cdot99}{10\cdot11\cdot12\cdot...\cdot99\cdot100}=\frac{9}{100}\)

Đáp án là \(-\frac{9}{100}\)nhá

Bài làm:

\(A=\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)

\(A=\frac{\left(-9\right)}{10}.\frac{\left(-10\right)}{11}.\frac{\left(-11\right)}{12}...\frac{\left(-98\right)}{99}.\frac{\left(-99\right)}{100}\)

\(A=-\left(\frac{9.10.11...98.99}{10.11.12...99.100}\right)\)

\(A=-\frac{9}{100}\)

Học tốt!!!!

\(\frac{1}{9x10}\)\(+\frac{1}{10x11}\)\(+\frac{1}{11x12}\)\(+.....\)\(+\frac{1}{805x806}\)

\(=\frac{1}{9}\)\(-\frac{1}{10}\)\(+\frac{1}{10}\)\(-\frac{1}{11}\)\(+\frac{1}{11}\)\(-\frac{1}{12}\)\(+.....\frac{1}{805}\)\(-\frac{1}{806}\)

\(=\frac{1}{9}\)\(-\frac{1}{806}\)

\(=\frac{797}{7254}\)

a,\(\frac{11}{12}-\left(\frac{5}{42}-x\right)=\frac{15}{28}-\frac{11}{12}\)

\(\Leftrightarrow\frac{11}{12}-\frac{5}{42}+x=\frac{15}{28}-\frac{11}{12}\)

\(\Leftrightarrow x=\frac{15}{28}-\frac{11}{12}-\frac{11}{12}+\frac{5}{42}\)

\(\Leftrightarrow x=\left(\frac{15}{28}+\frac{5}{42}\right)-\left(\frac{11}{12}+\frac{11}{12}\right)\)

\(\Leftrightarrow x=\frac{55}{84}-\frac{11}{6}\)

\(\Leftrightarrow x=\frac{-33}{28}\)

b, \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)

\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)

\(\Leftrightarrow x+1=0\)

\(\Leftrightarrow x=-1\)