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Ta có: \(A=\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{97}+\dfrac{1}{99}}{\dfrac{1}{1\cdot99}+\dfrac{1}{3\cdot97}+\dfrac{1}{5\cdot95}+...+\dfrac{1}{97\cdot3}+\dfrac{1}{99\cdot1}}\)
\(\Leftrightarrow\dfrac{A}{100}=\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{97}+\dfrac{1}{99}}{\dfrac{100}{1\cdot99}+\dfrac{100}{3\cdot97}+\dfrac{100}{5\cdot95}+...+\dfrac{100}{97\cdot3}+\dfrac{100}{99\cdot1}}\)
\(\Leftrightarrow\dfrac{A}{100}=\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{97}+\dfrac{1}{99}}{1+\dfrac{1}{99}+\dfrac{1}{3}+\dfrac{1}{97}+\dfrac{1}{5}+\dfrac{1}{95}+...+\dfrac{1}{97}+\dfrac{1}{3}+\dfrac{1}{99}+1}\)
\(\Leftrightarrow\dfrac{A}{100}=\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{97}+\dfrac{1}{99}}{2\left(1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{97}+\dfrac{1}{99}\right)}\)
\(\Leftrightarrow\dfrac{A}{100}=\dfrac{1}{2}\)
hay A=50
Đặt A = \(\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)
\(\dfrac{1}{7}A=\dfrac{1}{7}\left(\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\right)\)
\(=\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{13}{15.28}\)
\(=\dfrac{7-2}{2.7}+\dfrac{11-7}{7.11}+\dfrac{14-11}{11.14}+\dfrac{15-14}{14.15}+\dfrac{28-15}{15.28}\)
\(=\dfrac{7}{2.7}-\dfrac{2}{2.7}+\dfrac{11}{7.11}-\dfrac{7}{7.11}+\dfrac{14}{11.14}-\dfrac{11}{11.14}+\dfrac{15}{14.15}-\dfrac{14}{14.15}+\dfrac{28}{15.28}-\dfrac{15}{15.28}\)
\(=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{28}\)
\(=\dfrac{1}{2}-\dfrac{1}{28}=\dfrac{14}{28}-\dfrac{1}{28}=\dfrac{13}{28}\)
\(A=\dfrac{13}{28}\div\dfrac{1}{7}=\dfrac{13}{4}\)
Đặt A = \(\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)
\(\Rightarrow\dfrac{1}{7}.A=\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{13}{15.28}\)
\(\Rightarrow\dfrac{1}{7}.A=\left(\dfrac{1}{2}-\dfrac{1}{7}\right)+\left(\dfrac{1}{7}-\dfrac{1}{11}\right)+\left(\dfrac{1}{11}-\dfrac{1}{14}\right)+\left(\dfrac{1}{14}-\dfrac{1}{15}\right)+\left(\dfrac{1}{15}-\dfrac{1}{28}\right)\)
\(\Rightarrow\dfrac{1}{7}.A=\dfrac{1}{2}-\dfrac{1}{28}=\dfrac{13}{28}\)
\(\Leftrightarrow A=\dfrac{13}{4}\)
Vậy...................
Ta có : \(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times.....\times1\frac{1}{2017}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{2018}{2017}\)
\(=\frac{2018}{2}=1009\)
\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times....\times1\frac{1}{2017}\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{2018}{2017}\)
\(=\frac{3\times4\times5\times.....\times2018}{2\times3\times4\times.....\times2017}\)
\(=\frac{2018}{2}=1009\)
\(=\frac{3}{2}\times\frac{4}{3}\times.............\times\frac{2016}{2015}\)
\(=\frac{3\times4\times.............\times2016}{2\times3\times..............\times2015}\)
\(=\frac{2016}{2}=1008\)
A=\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}....1\frac{1}{2015}\)
A=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{2016}{2015}\)
A=\(\frac{3.4.5.....2016}{2.3.4....2015}\)
A=\(\frac{2016}{2}=1008\)
nhanh tay lên các bạn ai trả lời đầu tiên mình cho 5 cái tick
\(A=1\frac{1}{2}.1\frac{1}{3}....1\frac{1}{2015}\)
\(=\frac{3}{2}.\frac{4}{3}......\frac{2016}{2015}\)
\(=\frac{2016}{2}=1008\)
\(A=1\frac{1}{2}\cdot1\frac{1}{3}\cdot1\frac{1}{4}\cdot...\cdot1\frac{1}{2015}\)
\(\Rightarrow A=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{2016}{2015}\)
\(\Rightarrow A=\frac{3\cdot4\cdot5\cdot...\cdot2016}{2\cdot3\cdot4\cdot...\cdot2015}=\frac{2016}{2}=1008\)
Vậy A = 1008
=4/3 x 9/8 x 16/15 x 25/24x.....x100/99 =2x2x3x3x4x4x5x5x.....x10x10/1x3x2x4x3x5x4x6x....x9x11
=(2x3x4x5x....x10 ) x (2x3x4x5x...x10) / (1x2x3x4x....x9 ) x (3x4x5x...x11)
=10x2/11 =20/11
\(\dfrac{4}{3}\times\dfrac{9}{8}\times\dfrac{16}{15}\times\dfrac{25}{24}\times.....\times\dfrac{100}{99}\)
\(\dfrac{2x2x3x3x4x4x5x5x.....x10x10}{1x3x2x4x3x5x4x6x...9x11}\)
\(=\dfrac{10x2}{11}=\dfrac{20}{11}\)