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\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{2015}\right)\)
\(=\left(\frac{2-1}{2}\right)\left(\frac{3-1}{3}\right)\left(\frac{4-1}{4}\right)....\left(\frac{2015-1}{2015}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2013}{2014}.\frac{2014}{2015}\)
\(=\frac{1}{2015}\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2014}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2013}{2014}\)
\(=\frac{1}{2014}>\frac{1}{2015}\)
\(1\frac{1}{2}x1\frac{1}{3}x1\frac{1}{4}x..........x1\frac{1}{2015}\)
\(=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x.........x\frac{2016}{2015}\)
\(=\frac{2016}{2}=1008\)
a)\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}......\frac{99}{100}\)
\(=\frac{1.2.3.4.....99}{2.3.4.5.6.....100}\)
\(=\frac{1}{100}\)
b) Tương tự như câu a
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2015}\right)\times\left(1-\frac{1}{2016}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2014}{2015}\times\frac{2015}{2016}\)
\(=\frac{1}{2016}\)
Giải : Ta có (1-1/2)*(1-1/3)*(1-1/4)*....*(1-1/2015)*(1-1/2016)
= 1* -(1/2+1/3+1/4+....+1/2015+1/2016)
= 1* - (1/2+1/2016 +1/3+1/2015 +...+1/1007)
= 1* -(1/2033134)
= -1/2033134
\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}...1\frac{1}{9}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{10}{9}\)
\(=\frac{10}{2}=5\)
DẤU . LÀ DẤU NHÂN NHA BẠN
\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\times1\frac{1}{9}\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\times\frac{10}{9}\)
\(=\frac{3\times4\times5\times6\times7\times8\times9\times10}{2\times3\times4\times5\times6\times7\times8\times9}=\frac{10}{2}=5\)
~ Hok tốt ~
(1-1/2)x(1-1/3)x.....x(1-1/2014)x(1-1/2015)
=1/2x2/3x.....x2013/2014x2014/2015
=1/2015