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\(\left(1\frac{1}{7}\right)\left(1\frac{1}{8}\right)\left(1\frac{1}{9}\right)...\left(1\frac{1}{50}\right)\)
\(=\frac{8}{7}.\frac{9}{8}.\frac{10}{9}...\frac{51}{50}\)
\(=\frac{8.9.10...51}{7.8.9...50}\)
\(=\frac{51}{7}\)
\(=\frac{8}{7}\times\frac{9}{8}\times\frac{10}{9}\times...\times\frac{51}{50}\)
\(=\frac{51}{7}\)
Ta có ; \(1\dfrac{1}{10}.1\dfrac{1}{11}.....1\dfrac{1}{2011}.1\dfrac{1}{2012}\)
\(=\dfrac{11}{10}.\dfrac{12}{11}.....\dfrac{2012}{2011}.\dfrac{2013}{2012}\)
\(=\dfrac{2013}{10}=201,3\)
1 \(\dfrac{1}{10}\)x 1\(\dfrac{1}{11}\)x 1\(\dfrac{1}{12}\) x...x 1\(\dfrac{1}{2011}\)x 1\(\dfrac{1}{2012}\)
=\(\dfrac{11}{10}\)x \(\dfrac{12}{11}\)x \(\dfrac{13}{12}\)x \(\dfrac{2012}{2011}\)x \(\dfrac{2013}{2012}\)
\(1\frac{1}{7}\cdot1\frac{1}{8}\cdot1\frac{1}{9}\cdot...\cdot1\frac{1}{50}\)
\(=\frac{8}{7}\cdot\frac{9}{8}\cdot\frac{10}{9}\cdot...\cdot\frac{51}{50}\)
\(=\frac{8\cdot9\cdot10\cdot...\cdot51}{7\cdot8\cdot9\cdot...\cdot50}\)
\(=\frac{51}{7}\)
A=(6 : 35−116 x 67) : (415 x 1011+5211)A=(6 : 35−116 x 67) : (415 x 1011+5211)
A=(6 : 35−76 x 67) : (215 x 1011+5711)A=(6 : 35−76 x 67) : (215 x 1011+5711)
A=(10−1) : (4211+5711)A=(10−1) : (4211+5711)
A=9 : 9A=9 : 9
A=1
a) 1+2+3+...+2018
=[(2018-1):1+1].(2018+1):2
=2018.2019:2
=2037171
b) 4+7+10+13+...+2017
=[(2017-4):3+1].(2017+4):2
=672.2021:2
=679056
c) 1+2-3-4+5+6-7-8+9+10-11-12+13+14
=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+13+14
=-4+(-4)+(-4)+13+14
=-12+27
=15
d) 23 x 75 + 25 x 23 + 180
=23 x (75+25) +180
=23 x 100 +180
=2300+180
2480
chúc ban hoc tốt nha
a) Số số hạng: ( 2018 - 1 ) : 1 + 1 = 2018
Tổng: 2018 x ( 2018 + 1 ) : 2 = 2 037 171
\(1\dfrac{1}{7}\times1\dfrac{1}{8}\times1\dfrac{1}{9}\times1\dfrac{1}{10}\times1\dfrac{1}{11}\times1\dfrac{1}{12}\times1\dfrac{1}{13}\)
\(=\dfrac{8}{7}\times\dfrac{9}{8}\times\dfrac{10}{9}\times\dfrac{11}{10}\times\dfrac{12}{11}\times\dfrac{13}{12}\times\dfrac{14}{13}\)
\(=\dfrac{8\times9\times10\times11\times12\times13\times14}{7\times8\times9\times10\times11\times12\times13}\)
\(=\dfrac{1\times1\times1\times1\times1\times1\times2}{1\times1\times1\times1\times1\times1\times1}\)
\(=2\)