tính nhanh: \(1\frac{1}{4}\times1\frac{1}{8}\times1\frac{1}{15}\times1\frac{1}{24}\times1\frac{1}{35}\times...\times1\frac{1}{9800}\)
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\(=\frac{16}{15}\times\frac{17}{16}\times\frac{18}{17}\times...\times\frac{2010}{2009}\times\frac{2011}{2010}\)
\(=\frac{1}{15}\times2011\)
\(=\frac{2011}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1 1/13 x 1 1/14 x ........... x 1 1/2014 = 14/13 x 15/14 x ...... x 2015/2014 = (14 x 15 x ....x 2014) x 2015/( 14 x 15 x .......x2014) x 13 = 2015/13
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}.1\frac{1}{6}.1\frac{1}{7}.1\frac{1}{8}.1\frac{1}{9}.1\frac{1}{10}.1\frac{1}{11}\)
\(=\frac{4}{3}.\frac{5}{4}.\frac{6}{5}.\frac{7}{6}.\frac{8}{7}.\frac{9}{8}.\frac{10}{9}.\frac{11}{10}.\frac{12}{11}\)
\(=\frac{12}{3}=4\)
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a)
12,5 x 40,7 + 59,3 x12,5
= 12,5 x ( 40,7 + 59,3)
= 12,5 x 100
= 1250
a]
12,5 x 40,7 + 59,3 x 12,5
= 12,5 x [ 40,7 + 59,3]
= 12,5 x 100 = 125
b]
1,9 + 1,8 + 1,7 + 1,6 + 1,5 , 1,4 , 1,3 , 1,2 , 1,1
= [1,9 + 1,1 ] + [1,8 + 1,2 ] + [ 1,7 + 1,3 ] + [1,6 + 1,4 ] + 1,5
= [3 + 3 + 3 + 3 ]+ 1,5
= 12 + 1,5
=13,5
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times.....\times1\frac{1}{2017}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{2018}{2017}\)
\(=\frac{2018}{2}=1009\)
\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times....\times1\frac{1}{2017}\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{2018}{2017}\)
\(=\frac{3\times4\times5\times.....\times2018}{2\times3\times4\times.....\times2017}\)
\(=\frac{2018}{2}=1009\)