tính A=20/21 *27/28*35/36*.....*464/465
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17 tháng 8 2015
Dấu chấm là dấu nhân
\(1+\frac{2}{3}+\frac{5}{6}+\frac{9}{10}+...+\frac{44}{45}\)
\(=1+1-\frac{1}{3}+1-\frac{1}{6}+1-\frac{1}{10}+...+1-\frac{1}{45}\)
\(=8-2\cdot\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{9\cdot10}\right)\)
\(=8-2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-2\cdot\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=8-2\cdot\frac{2}{5}\)
\(=8-\frac{4}{5}\)
\(=\frac{36}{5}\)
DN
18 tháng 8 2015
Đặt \(A=1+\frac{2}{3}+\frac{5}{6}+\frac{9}{10}+\frac{20}{21}+\frac{27}{28}+\frac{35}{36}+\frac{44}{45}\)
\(=1+1-\frac{1}{3}+1-\frac{1}{6}+1-\frac{1}{10}+1-\frac{1}{21}+1-\frac{1}{28}+1-\frac{1}{36}+1-\frac{1}{45}\)
\(=8-\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\right)\)
\(\Leftrightarrow\frac{1}{2}.A=4-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=4-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=4-\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{6}-\frac{1}{10}\right)\)
\(=4-\frac{11}{30}=\frac{109}{30}\)
\(\Rightarrow A=\frac{109}{15}\)
30 tháng 8 2023
\(\dfrac{2}{3}+\dfrac{5}{6}+\dfrac{9}{10}+\dfrac{14}{15}+\dfrac{20}{21}+\dfrac{27}{28}+\dfrac{35}{36}+\dfrac{44}{45}\\ =\left(1-\dfrac{1}{3}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{10}\right)+\left(1-\dfrac{1}{15}\right)+\left(1-\dfrac{1}{21}\right)+\left(1-\dfrac{1}{28}\right)+\left(1-\dfrac{1}{36}\right)+\left(1-\dfrac{1}{45}\right)\\ =8-\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}\right)\\ =8-\left(\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+\dfrac{2}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\\ =8-\left(\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}+\dfrac{2}{7.8}+\dfrac{2}{8.9}+\dfrac{2}{9.10}\right)\\ =8-2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\\ =8-2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =8-2\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=8-2.\dfrac{2}{5}=8-\dfrac{4}{5}=\dfrac{36}{5}\)
3 tháng 5 2018
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37
=(1+37)x37:2
=703
H
17 tháng 9 2023
`a) 465 + [ 58 + ( -465 ) + ( -38 ) ]`
`= 465 + 58 - 465 -38`
`= (465-465) + (58-38)`
`=0+ 20`
`=20`
`b) ( 35 - 17 ) + ( 17 + 20 - 35 )`
`= 35 -17 +17 +20-35`
`= (35-35) + (-17+17)+20`
`= 0 + 0 +20`
`=20`
18 tháng 9 2023
a)465+[58+(−465)+(−38)]
=465+58−465−38=465+58−465−38
=(465−465)+(58−38)=(465−465)+(58−38)
=0+20=0+20
=20=20
�)(35−17)+(17+20−35)b)(35−17)+(17+20−35)
=35−17+17+20−35=35−17+17+20−35
=(35−35)+(−17+17)+20=(35−35)+(−17+17)+20
=0+0+20=0+0+20
=20=20