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HS
3
CV
1 tháng 8 2017
Đặt A = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
\(\frac{1}{2}A=\frac{1}{2}+\frac{1}{6}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(A=\frac{9}{10}.2\)
\(=\frac{9}{5}\)
1 tháng 8 2017
Đặt \(A=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
=> \(\frac{1}{2}A=\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{45}\right).\frac{1}{2}\)
\(=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{9.10}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{10}\)
= \(1-\frac{1}{10}=\frac{9}{10}\)
=> A= 9/10:1/2=9/5
NB
1
KZ
27 tháng 2 2022
a, \(\frac{3}{10}+\frac{5}{8}=\frac{24}{80}+\frac{50}{80}=\frac{74}{80}=\frac{37}{40}\)
b, \(\frac{1}{8}+\frac{5}{6}=\frac{3}{24}+\frac{20}{24}=\frac{23}{24}\)
c, \(\frac{1}{3}+\frac{1}{6}+\frac{1}{8}=\frac{8}{24}+\frac{4}{24}+\frac{3}{24}=\frac{15}{24}=\frac{5}{8}\)
#Fox
H
3 tháng 3 2023
`4/7+4`
`=4/7+4/1`
`=4/7+28/7`
`=32/7`
__
`3+6/11`
`=33/11+6/11`
`=39/11`
__
`3-5/7`
`=3/1-5/7`
`=21/7-5/7`
`=16/7`
__
`21/9-2`
`=21/9-18/9`
`=3/9`
`=1/3`
__
`15/24+2`
`=15/24+48/24`
`=63/24`
`=21/16`
__
`63/45-20/25`
`=63/45-4/5`
`=63/45-36/45`
`=27/45`
`=9/15`
__
`3/4-2/8`
`=3/4-1/4`
`=2/4`
__
`6/7-5/8`
`=48/56-35/56`
`=13/56`
__
`37/45-5/9`
`=37/45-25/45`
`=12/45`
`=4/15`
__
`46/39-11/13`
`=46/39-33/39`
`=13/39`
`=1/2`
__
`5/12+3/4+1/3`
`=5/12+9/12+4/12`
`=14/12+4/12`
`=18/12`
`=3/2`
__
`1/2+3/7+11/14`
`=7/14+6/14+11/14`
`=13/14+11/14`
`=24/14`
`=12/7`
__
`7/10-(1/5+1/4)`
`=7/10-(4/20+5/20)`
`=7/10-9/20`
`=14/20-9/20`
`=5/20`
`=1/4`
__
`15/4-2/3-3/4`
`=(15/4-3/4)-2/3`
`=12/4-2/3`
`=3-2/3`
`=9/3-2/3`
`=7/3`
BN
8
DP
2 tháng 8 2017
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{9.10}\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=2.\frac{2}{5}=\frac{4}{5}\)
LH
2 tháng 8 2017
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{9.10}\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{4}{5}\)
10 tháng 1
\(C=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{5050}\)
\(=2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{10100}\right)\)
\(=2\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{100\cdot101}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{100}-\dfrac{1}{101}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{101}\right)\)
\(=2\cdot\dfrac{99}{202}=\dfrac{99}{101}\)
A = 1/3 + 1/6 +1/10 +1/15 +.....+1/45
A = 2/6 + 2/12+2/20+2/30 +.....+2/90
A = 2(\(\dfrac{1}{2.3}\)+ \(\dfrac{1}{3.4}\)+ \(\dfrac{1}{4.5}\)+\(\dfrac{1}{5.6}\)+.....+\(\dfrac{1}{9.10}\))
A = 2(1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +1/5 -1/6 +....+1/9-1/10)
A =2(\(\dfrac{1}{2}\) - \(\dfrac{1}{10}\))
A = 2. \(\dfrac{2}{5}\)
A = 4/5
(dấu . là phép nhân)
13+16+110+115+...+14513+16+110+115+...+145
=2×(16+112+120+130+...+190)=2×(16+112+120+130+...+190)
=2×(12×3+13×4+14×5+...+19×10)=2×(12×3+13×4+14×5+...+19×10)
=2×(12−13+13−14+14−15+...+19−110)=2×(12−13+13−14+14−15+...+19−110)
=2×(12−110)=2×(12−110)
=45