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`A=-5/(1.6)-5/(6.11)-5/(11.16)-...-5/(2006.2011)`
`-A=5/(1.6)+5/(6.11)+5/(11.16)+...+5/(2006.2011)`
`-A=1-1/6+1/6-1/11+1/11-1/16+.....+1/2006-1/2011`
`-A=1-1/2011=2010/2011`
`A=-2010/2011`
a,1/1-1/4+1/4-1/7+...+1/2008-1/2011
=(1-1/2011)+(-1/4+1/4)+...+(-1/2008+1/2008)
=1-1/2011+0+...+0
=1-1/2011
=2010/2011
\(B=\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{5n+1}+\frac{1}{5n+6}\)
\(B=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-...+\frac{1}{5n+1}-\frac{1}{5n+6}\)
\(B=\frac{1}{1}-\frac{1}{5n+6}=\frac{5n+5}{5n+6}\)
= 2/5 x (1/1 -1/6) + 2/5 x (1/6 - 1/11) + 2/5 x (1/11-1/16)+....+2/5 x (1/2021 - 1/2026)
= 2/5 x( 1/1 - 1/6 + 1/6 - 1/11+1/11-1/16+....+1/2021 - 1/2026)
= 2/5 x ( 1/1- 1/2026 )
=2/5 x ( 2026/2026 - 1/2026 )
=2/5 x 2025/2026
= 4050/10130 = 1013/405
thấy đúng thì cho mình ( đúng dưới câu trả lời nha )
=1/5(5/1*6+5/6*11+...+5/101*106)
=1/5(1-1/6+1/6-1/11+...+1/101-1/106)
=1/5(1-1/106)
=1/5*105/106
=21/106
\(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+...+\dfrac{1}{101.106}\)
\(B=\dfrac{1}{5}.\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)
\(B=\dfrac{1}{5}.\left(1-\dfrac{1}{106}\right)\)
\(B=\dfrac{1}{5}.\dfrac{105}{106}\)
\(B=\dfrac{21}{106}\)
5S=5.(1/1.6+1/6.11+...+1/496.501)
5S=5/1.6+5/6.11+...+5/496.501
5S=1/1-1/6+1/6-1/11+...+1/496-1/501
5S=1-1/501
5S=500/501
S=500/501:5=100/501
k nhé
ta co:5S=5/1.6+5/6.11+5/11.16+...+5/496.501
=1-1/6+1/6-1/11+1/11-1/16+.....+1/496-1/501
=1-1/501=500/501
=>S=500/501:5=100/501
MK đau tien nha bn
1/1.6 + 1/6.11+ 1/11.16+ ....
số thứ 100 có dạng 1/(496.501)
do đó tổng trên bằng :
1/5( 1/1- 1/501)
= 100/ 501
đặt \(A=\dfrac{1}{1.6}+\dfrac{1}{6.11}+....+\dfrac{1}{2006.2011}\)
=>\(6A=\dfrac{6}{1.6}+\dfrac{6}{6.11}+....+\dfrac{6}{2006.2011}\)
=>\(6A=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+....+\dfrac{1}{2006}-\dfrac{1}{2011}\)
=> \(6A=1-\dfrac{1}{2011}\)
=> \(6A=\dfrac{2011-1}{2011}\)
=> \(6A=\dfrac{2010}{2011}\)
=> A = \(\dfrac{2010}{2011}.\dfrac{1}{6}\)
=> A=\(\dfrac{335}{2011}\)
\(\dfrac{1}{1.6}+\dfrac{1}{6.11}+...+\dfrac{1}{2006.2011}\)
\(=\dfrac{1}{6}.\left(\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{2006}-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{6}.\left(\dfrac{1}{1}-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{6}.\left(\dfrac{2011}{2011}-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{6}.\dfrac{2010}{2011}\)
\(=\dfrac{335}{2011}\)
\(\Rightarrow\dfrac{335}{2011}\)