Tính nhanh
A= 1/6+1/10+1/15+...+1/210
K
Khách
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28 tháng 1 2021
a. -37 + 54 + -70+ -163 + 246
= ( 54 + 246) + (-37 - 163 ) - 70
= 300 -200 - 70 = 30
b. -359+ 181+ -123+ 350+ -172
=(-178)+227+(-172)
=49+(-172)
=-123
c.-69+ 53+ 46+ -94+-14+ 78
=(-16)+(-48)+64
=-64+64
=0
d. 13- 12+ 11+10- 9+ 8- 7- 6+ 5- 4+ 3+2- 1
= 13 - (13 - 1) + (13 - 2) + (13 - 3) - (13 - 4) + (13 - 5) - (13 - 6) - (13 - 7) + (13 - 8) - (13 - 9) + (13 - 10) + (13 - 11) - (13 - 12)
= 13 - 13 + 1 + 13 - 2 + 13 - 3 - 13 + 4 + 13 - 5 - 13 + 6 - 13 + 7 + 13 - 8 - 13 + 9 + 13 - 10 + 13 - 11 - 13 + 12
= (13 - 13 + 13 + 13 - 13 + 13 - 13 - 13 + 13 - 13 + 13 + 13 - 13) + (1 - 2 - 3 + 4 - 5 + 6 + 7 - 8 + 9 - 10 - 11 = 12)
= 13 + 0
= 13
28 tháng 1 2021
a) \(-37+54+\left(-70\right)+\left(-163\right)+246\)
\(=\left(246+54\right)-\left(37+163\right)-70\)
\(=300-200-70\)
\(=100-70=30\)
b) \(-359+181+\left(-123\right)+350+\left(-172\right)\)
\(=-359+181-123+350-172\)
\(=\left(-359+350\right)+\left(181-172\right)-123\)
\(=-9+9-123\)
\(=-123\)
c) \(-69+53+46+\left(-94\right)+\left(-14\right)+78\)
\(=-69+53+46-94-14+78\)
\(=\left(-69+78\right)+\left(53-14\right)+\left(46-94\right)\)
\(=9+39-48\)
\(=48-48=0\)
d) \(13-12+11+10-9+8-7-6+5-4+3+2-1\)
\(=\left(13-12\right)+\left(11+10\right)-\left(9-8\right)-\left(7+6\right)+\left(5-4\right)+\left(3+2-1\right)\)
\(=1+21-1-13+1+5\)
\(=21-13+1+5\)
\(=8+1+5=9+5=14\)
ND
1
14 tháng 7 2023
A=1+1/2+1/3+1/6+(1/12+1/15+1/20+1/30)+1/35
=71/35+7/30=95/42
XO
3 tháng 3 2020
C = \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)...\left(1-\frac{1}{210}\right)=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}...\frac{209}{210}=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{418}{420}\)
= \(\frac{2.2}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{19.22}{20.21}=\frac{2.2\left(2.3.4...19\right)\left(5.6...22\right)}{\left(2.3.4..20\right)\left(3.4.5..21\right)}=\frac{4.22}{19.3.4}=\frac{22}{57}\)
K
1
20 tháng 4 2016
Mình tính đc kết quả 22 nhưng hơi khó hiểu mong mọi người giải dùm
28 tháng 2 2022
\(a,\left(1-\dfrac{1}{10}\right)\times\left(1-\dfrac{1}{11}\right)\times\left(1-\dfrac{1}{12}\right)\times\left(1-\dfrac{1}{13}\right)\times\left(1-\dfrac{1}{14}\right)\times\left(1-\dfrac{1}{15}\right)=\dfrac{9}{10}\times\dfrac{10}{11}\times\dfrac{11}{12}\times\dfrac{12}{13}\times\dfrac{13}{14}\times\dfrac{14}{15}=\dfrac{9}{15}=\dfrac{3}{5}\)
\(b,\dfrac{2013\times2012-2}{2011+2011\times2013}=\dfrac{\left(2014-1\right)\times2012-2}{2011\times\left(2013+1\right)}=\dfrac{2014\times2012-2012-2}{2011\times2014}=\dfrac{2014\times2012-2014}{2011\times2014}=\dfrac{2014\times\left(2012-1\right)}{2011\times2014}=\dfrac{2011\times2014}{2011\times2014}=1\)
K
6
TA
22 tháng 4 2016
đặt A=(1-1/3)........
Ta có A=\(\frac{2}{3}\cdot\frac{5}{6}\cdot\frac{9}{10}\cdot...\cdot\frac{209}{210}=\frac{4}{6}\cdot\frac{10}{12}\cdot\frac{18}{20}\cdot...\cdot\frac{418}{420}=\frac{1\cdot4}{2\cdot3}\cdot\frac{2\cdot5}{3\cdot4}\cdot\frac{3\cdot6}{4\cdot5}\cdot...\cdot\frac{19\cdot22}{20\cdot21}\)
=\(\frac{1\cdot4\cdot2\cdot5\cdot3\cdot6\cdot...\cdot19\cdot22}{2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot...\cdot20\cdot21}=\frac{\left(1\cdot2\cdot3\cdot...\cdot19\right)\cdot\left(4\cdot5\cdot6\cdot...\cdot22\right)}{\left(2\cdot3\cdot4\cdot...\cdot20\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot21\right)}\)
=\(\frac{1\cdot22}{20\cdot3}=\frac{11}{30}\)
LC
22 tháng 4 2016
Đặt \(A=\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{210}\right)\)
=>\(A=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{209}{210}\)
=>\(A=\frac{2.2}{3.2}.\frac{5.2}{6.2}.\frac{9.2}{10.2}.\frac{14.2}{15.2}...\frac{209.2}{210.2}\)
=>\(A=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{418}{420}\)
=>\(A=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{19.22}{20.21}\)
=>\(A=\frac{\left(1.4\right).\left(2.5\right).\left(3.6\right).\left(4.7\right)...\left(19.22\right)}{\left(2.3\right).\left(3.4\right).\left(4.5\right).\left(5.6\right)...\left(20.21\right)}\)
=>\(A=\frac{\left(1.2.3.4...19\right).\left(4.5.6.7...22\right)}{\left(2.3.4.5...20\right).\left(3.4.5.6...21\right)}\)
=>\(A=\frac{1.22}{20.3}\)
=>\(A=\frac{22}{60}=\frac{11}{30}\)
Vậy \(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{210}\right)=\frac{11}{30}\)
LT
0
A = \(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{210}\)
\(\frac{1}{2}A=\frac{1}{2}\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{210}\right)\)
\(\frac{1}{2}A=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{420}\)
\(\frac{1}{2}A=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{20.21}\)
\(\frac{1}{2}A=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{20}-\frac{1}{21}\)
\(\frac{1}{2}A=\frac{1}{3}-\frac{1}{21}\)
\(\frac{1}{2}A=\frac{2}{7}\)
A = \(\frac{2}{7}:\frac{1}{2}\)
A = \(\frac{4}{7}\)