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\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2011.2012}\)
\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2011}-\frac{1}{2012}\)
\(S=1-\frac{1}{2012}\)
\(S=\frac{2011}{2012}\)
Chúc bạn học tốt nha !!!
=1-1/2+1/2-1/3+1/3-1/4+...+1/2011-1/2012
= 1-1/2012
= 2011/2012
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\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{2015.2016}\)
\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{2015}-\frac{1}{2016}\)
\(S=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)
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=> 3S = 1.2.3 + 2.3.3 + 3.4.3 + .... + 2011.2012.3
=> 3S = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + .... + 2011.2012.( 2013 - 2010 )
=> 3S = 1.2.3 + 2.3.4 - 1.2.3 + .... + 2011.2012.2013 - 2010.2011.2012
=> 3S = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 2010.2011.2012 - 2010.2011.2012 ) + 2011.2012.2013
=> 3S = 2011.2012.2013
=> S = ( 2011.2012.2013 ) : 3
3S=1.2.3+2.3.(4-1)+...............+2011.2012.(2013-2010)
3S=1.2.3+2.3.4-1.2.3+...............+2011.2012.2013-2010.2011.2012
3S=2011.2012.2013
S=2011.2012.2013:3
S=2714954572
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ta có \(3S=1\cdot2\cdot3+2\cdot3\cdot3+.....+99\cdot100\cdot3\)
\(3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)....+99\cdot100\cdot\left(101-98\right)\)
\(3S=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-......-98\cdot99\cdot100+99\cdot100\cdot101\)
\(3S=99.100.101\)
\(S=\frac{99\cdot100\cdot101}{3}\)
S=...
3S=1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3
3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100
3S=99.100.101
S=33.100.101
S=333300
Vậy S=333300
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