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( 1-1/2) . (1-1/3).(1-1/4).......(1-1/2016) . (1-1/2017)
=1/2.2/3.3.4x...x2015/2016.2016/2017
=1.2.3.4. ... .2015.2016/2.3.4.5. ... .2016.2017
(giống nhau bạn gạch đi )
=1/2017
\(A=\frac{2}{3}+\frac{1}{3}+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)
\(A=\left(\frac{2}{3}+\frac{1}{3}\right)+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)
\(A=1+\left(\frac{5}{75}+\frac{1}{75}\right)+\frac{1}{375}+\frac{1}{1875}\)
\(A=1+\frac{6}{75}+\frac{1}{375}+\frac{1}{1875}\)
\(A=1+\left(\frac{150}{1875}+\frac{1}{1875}\right)+\frac{1}{375}\)
\(A=1+\frac{151}{1875}+\frac{1}{375}\)
\(A=1+\left(\frac{151}{1875}+\frac{5}{1875}\right)\)
\(A=1+\frac{156}{1875}\)
\(A=\frac{1875}{1875}+\frac{156}{1875}\)
\(A=\frac{677}{625}\)
\(A=\frac{2}{3}+\frac{1}{3}+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)
\(\Leftrightarrow A=\left(\frac{2}{3}+\frac{1}{3}\right)+\left(\frac{1}{15}+\frac{1}{75}\right)+\left(\frac{1}{375}+\frac{1}{1875}\right)\)
\(\Leftrightarrow A=1+\left(\frac{5}{75}+\frac{1}{75}\right)+\left(\frac{5}{1875}+\frac{1}{1875}\right)\)
\(\Leftrightarrow A=1+\frac{6}{75}+\frac{6}{1875}\)
\(\Leftrightarrow A=1+\frac{2}{25}+\frac{2}{625}\)
\(\Leftrightarrow A=1+\left(\frac{2}{25}+\frac{2}{625}\right)\)
\(\Leftrightarrow A=1+\left(\frac{50}{625}+\frac{2}{625}\right)\)
\(\Leftrightarrow A=1+\frac{52}{625}\)
\(\Leftrightarrow A=\frac{677}{625}\)
a) ( 1/2-1/3-1/6).(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10
0.(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10
0+3/4.x = 9/10
3/4.x = 9/10
x = 9/10: 3/4
x = 6/5
b) x + ( 3/1.3+3/3.5+...+3/13.15) = 11/5
x + 3/2. ( 1-1/3 + 1/3 - 1/5 + ...+ 1/13 - 1/15) = 11/5
x + 3/2. ( 1-1/15) = 11/5
x + 3/2.14/15 = 11/5
x + 7/5 = 11/5
x = 11/5 - 7/5
x = 4/5
\(1\frac{1}{3}\cdot1\frac{1}{8}\cdot1\frac{1}{15}\cdot1\frac{1}{24}\cdot...\cdot1\frac{1}{99}\)
\(=\frac{4}{3}\cdot\frac{9}{8}\cdot\frac{16}{15}\cdot\frac{25}{24}\cdot...\cdot\frac{100}{99}\)
\(=\frac{2.2\cdot3.3\cdot4.4\cdot5.5\cdot...\cdot10.10}{1.3\cdot2.4\cdot3.5\cdot4.6\cdot...\cdot9.11}\)
\(=\frac{2.10}{1.11}=\frac{20}{11}\)
"." = nhân
a, \(\frac{1}{3}+0,75-50\%\)
\(=\frac{1}{3}+\frac{3}{4}-\frac{1}{2}\)
\(=\frac{13}{12}-\frac{1}{2}\)
\(=\frac{13}{12}-\frac{6}{12}=\frac{7}{12}\)
b, 40 x 0,25 : 2 + 12 x 0,5
= 40 : 4 : 2 + 12 : 2
= 10 : 2 + 12 : 2
= 5 + 6
= 11
Tính nhanh:
3/4 : 0,75 + 50% : 1/2 + 4/5 x 1 1/4
= 0,75 : 0,75 + 1/2 : 1/2 + 4/5 x 5/4
= 1 + 1 + 1
= 3
\(=\frac{3}{4}:\frac{3}{4}+\frac{1}{2}:\frac{1}{2}+\frac{4}{5}.\frac{5}{4}\)
\(=1+1+1\)
\(=3\)
Chúc bạn học tốt