3/4×8/9×15/16×....×120/121
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5 tháng 7 2016
Ta có:\(B=\frac{1.3}{2.2}x\frac{2.4}{3.3}x\frac{3.5}{4.4}x...x\frac{10.12}{11.11}\)
\(=\frac{1.2.3.4.5.6.7.8.9.10}{2.3.4.5.6.7.8.9.10.11}x\frac{3.4.5.6.7.8.9.10.11.12}{2.3.4.5.6.7.8.9.10.11}\)
\(=\frac{1}{11}x6\)
\(=\frac{6}{11}\)
Ai thấy đúng k nha.
DN
3
9 tháng 4 2015
\(A=1+\frac{1}{3}+1+\frac{1}{8}+1+\frac{1}{15}+...+1+\frac{1}{120}=\left(1+1+...+1\right)+\left(\frac{1}{1\times3}+\frac{1}{2\times4}+\frac{1}{3\times5}+...+\frac{1}{10\times12}\right)\)\(A=10+\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{2\times4}+\frac{2}{3\times5}+...+\frac{2}{10\times12}\right)=10+\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{12}\right)\)\(A=10+\frac{1}{2}\times\left(1+\frac{1}{2}+\left(-\frac{1}{3}+\frac{1}{3}\right)+\left(-\frac{1}{4}+\frac{1}{4}\right)+\left(-\frac{1}{5}+\frac{1}{5}\right)+...+\left(-\frac{1}{10}+\frac{1}{10}\right)-\frac{1}{11}-\frac{1}{12}\right)\)\(A=10+\frac{1}{2}\times\left(1+\frac{1}{2}-\frac{1}{11}-\frac{1}{12}\right)=10+\frac{175}{264}=\frac{2815}{264}\)
24 tháng 12 2023
`#3107.101107`
\(-16 \div (-8)+5[3-15\div5+2(-3+4)]\)
`= 2 + 5(3 - 3 - 6 + 8)`
`= 2 + 5*(-6 + 8)`
`= 2 + 5*2`
`= 2(5 + 1)`
`= 2*6 = 12`
____
`15*(-236)+15*235`
`= 15 * (-236 + 235)`
`= 15 * (-1)`
`= -15`
____
`237*(-28)+28*137`
`= 28 * (-237 + 137)`
`= 28 * (-100)`
`= -2800`
____
`(-3)*(-17)+3*(120-17)`
`= 3 * 17 + 3 * (120 - 17)`
`= 3 * (17 + 120 - 17)`
`= 3 * 120`
`= 360`
____
`(-8)*72+8*(-19)-(-8)`
`= 8 * (-72) + 8 * (-19) + 8`
`= 8 * (-72 - 19 + 1)`
`= 8 * (-90)`
`= -720`
24 tháng 12 2023
a)−16÷(−8)+5[3−15÷5+2(−3+4)]
=2+5(3−3−6+8)
=2+5⋅(−6+8)
=2+5⋅2
=2(5+1)
=2⋅6
=12
b)15⋅(−236)+15⋅235
=15⋅(−236+235)
=15⋅(−1)
=−15
c)237⋅(−28)+28⋅137
=28⋅(−237+137)
=28⋅(−100)
=−2800
d)(−3)⋅(−17)+3⋅(120−17)
=3⋅17+3⋅(120−17)
=3⋅(17+120−17)
=3⋅120
=360
e)(−8)⋅72+8⋅(−19)−(−8)
=8⋅(−72)+8⋅(−19)+8
=8⋅(−72−19+1)
=8⋅(−90)
=−720
NK
3
NK
Nguyễn Kim Tiến
VIP
24 tháng 7 2023
=2x2/1x3 x 3x3/2x4x4/3x5 x ... x 11x11/10x12
=2x2x3x3x4x4x...x11x11/1x3x2x4x3x5x...x10x12
= 2x3x4x...x11)x(2x3x4x...x11)/(1x2x3x4x...x11)/(1x2x3x...x10)x(2x3x4x...x11)
=11x2/1x12
=22/12
=11/6
24 tháng 7 2023
4/3x9/8x16/15x...x121/120=\(\dfrac{2^2}{1\cdot3}\)x\(\dfrac{3^2}{2\cdot4}\)x\(\dfrac{4^2}{3\cdot5}\)x...x\(\dfrac{11^2}{10\cdot12}\)=\(\dfrac{2}{3}\)x\(\dfrac{11}{10}\)=\(\dfrac{11}{15}\)
HT
1
NV
5 tháng 10 2018
\(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{121}{120}.\frac{144}{143}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{11.11}{10.12}.\frac{12.12}{11.13}\)
\(=\frac{2.2.3.3.4.4.5.5...11.11.12.12}{1.3.2.4.3.5.4.6...10.12.11.13}\)
\(=\frac{\left(2.3.4.5...11.12\right).\left(2.3.4.5...11.12\right)}{\left(1.2.3.4...10.11\right).\left(3.4.5.6...12.13\right)}\)
\(=\frac{12.2}{1.13}\)
\(=\frac{24}{13}\)
( Dấu \(.\)là dấu \(\times\)nha )
VN
1
S
12 tháng 4 2023
\(\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot...\cdot\dfrac{400}{399}\)
\(=\dfrac{2\cdot2}{1\cdot3}\cdot\dfrac{3\cdot3}{2\cdot4}\cdot\dfrac{4\cdot4}{3\cdot5}\cdot...\cdot\dfrac{20\cdot20}{19\cdot21}\)
\(=\dfrac{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot20\cdot20}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot19\cdot21}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot20}{1\cdot2\cdot3\cdot...\cdot19}\cdot\dfrac{2\cdot3\cdot4\cdot...\cdot20}{3\cdot4\cdot5\cdot...\cdot21}\)
\(=20\cdot\dfrac{2}{21}\)
\(=\dfrac{40}{21}\)
PK
1
NK
Nguyễn Kim Tiến
VIP
24 tháng 7 2023
B=1x3/2x2x2x4/3x3x3x5/4x4x...x10x12/11x11
B=1x3x2x4x3x5x...x10x12/2x2x3x3x4x4x...x11x11
B=(1x2x3x...x10)x(2x3x5x...x12)/(2x3x4x...x11)x(2x3x4x...x11)
B=1x12/11x2
B=12/22
B=6/11
Vậy B = 6/11
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{120}{121}\)
\(=\frac{2.3.4......10}{2.3.4.....11}.\frac{3.4.5.....12}{2.3.4.....11}\)
\(=\frac{1}{11}.6=\frac{6}{11}\)