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\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)
\(=3.\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)
\(=3.A\)với \(A=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\)
\(\Rightarrow2^2A=\left(2+\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}\right)\)
\(\Rightarrow2^2A-A=\left(2+\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)
\(\Rightarrow4A-A=2-\frac{1}{2^9}\)
\(\Rightarrow3A=2-\frac{1}{512}=\frac{1023}{512}\Rightarrow A=\frac{1023}{512}:3\)
\(\Rightarrow\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}=3.\left(\frac{1023}{512}:3\right)=\frac{1023}{512}\)
\(1.a,\frac{5}{7}=\frac{5.9}{7.9}=\frac{45}{63};\frac{4}{9}=\frac{4.7}{9.7}=\frac{28}{63}.\)
\(b,\frac{7}{15},\frac{5}{3}=\frac{5.5}{3.5}=\frac{25}{15}\)
\(c,\frac{11}{12}=\frac{11.4}{12.4}=\frac{44}{48};\frac{7}{48}\)
\(d,\frac{3}{2}=\frac{3.3}{2.3}=\frac{9}{6};\frac{2}{3}=\frac{2.2}{3.2}=\frac{4}{6}\)
\(e,\frac{1}{3}=\frac{1.4}{3.4}=\frac{4}{12};\frac{5}{4}=\frac{5.3}{4.3}=\frac{15}{12};\frac{10}{12}\)
Mình không bày bn cách giải, nhưng sẽ gợi ý:
2 bài tương tự nhau, mẫu gấp nhau 3 lần nhé
\(\left(1-\frac{1}{6}\right)x\left(1-\frac{1}{7}\right)x\left(1-\frac{1}{8}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{10}\right)\)
\(=\frac{5}{6}x\frac{6}{7}x\frac{7}{8}x\frac{8}{9}x\frac{9}{10}\)
\(=\frac{1}{2}\)
=(1/1-1/6)x(1/1-1/7)x(1/1-1/8)x(1/1-19)x(1/1-1/10)
=5/6x6/6x7/8x8/9x9/10
\(\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)\(\\ \frac{1}{3}+\frac{2}{3}=1\)\(\frac{9}{10}+\frac{1}{10}=1\)
\(\frac{1}{3}+x\times\frac{2}{7}=\frac{11}{12}\)
\(x\times\frac{2}{7}=\frac{11}{12}-\frac{1}{3}\)
\(x\times\frac{2}{7}=\frac{7}{12}\)
\(x=\frac{7}{12}:\frac{2}{7}\)
\(x=\frac{49}{24}\)
~Moon~
\(\frac{1}{3}+x.\frac{2}{7}=\frac{11}{12}\)
\(x.\frac{2}{7}=\frac{11}{12}-\frac{1}{3}\)
\(x.\frac{2}{7}=\frac{7}{12}\)
\(x=\frac{7}{12}\div\frac{2}{7}\)
\(x=\frac{49}{24}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=1-\left(\frac{1}{2}-\frac{1}{2}\right)-\left(\frac{1}{3}-\frac{1}{3}\right)-......-\left(\frac{1}{6}-\frac{1}{6}\right)-\frac{1}{7}\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
1/2+1/6+1/12+1/20+1/30+1/42
=1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)
\(=\frac{3}{2}\times\frac{4}{3}\times...\times\frac{100}{99}\)
\(=\frac{100}{2}=50\)
ilhyhioubv;p
1/2 + 1/4 + 1/12 + 9/7
= 89/42