tính tổng sau: 1/1×6 + 1/6×11 + 1/11×16 + 1/16×21 + ……. + 1/2006×2011 + 1/2011×2016 13/09/2021 Bởi Quinn tính tổng sau: 1/1×6 + 1/6×11 + 1/11×16 + 1/16×21 + ……. + 1/2006×2011 + 1/2011×2016
`1/1.6+1/6.11+1/11.16+…+1/2011.2016` `=1/5(5/1.6+5/6.11+5/11.16+…+5/2011.2016)` `=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/2011-1/2016)` `=1/5(1-1/2016)` `=1/5 . 2015/2016` `=403/2016` Bình luận
$\frac{1}{1.6}$ + $\frac{1}{6.11}$ + $\frac{1}{11.16}$ + $\frac{1}{16.21}$ +…+ $\frac{1}{2006.2011}$ + $\frac{1}{2011.2016}$ = $\frac{1}{5}$ . ($\frac{5}{1.6}$ + $\frac{5}{6.11}$ + $\frac{5}{11.16}$ + $\frac{5}{16.21}$ +…+ $\frac{5}{2006.2011}$ + $\frac{5}{2011.2016}$) = $\frac{1}{5}$ . ($\frac{1}{1}$ – $\frac{1}{6}$ + $\frac{1}{6}$ – $\frac{1}{11}$ + $\frac{1}{11}$ – $\frac{1}{16}$ + $\frac{1}{16}$ – $\frac{1}{21}$ +…+ $\frac{1}{2006}$ – $\frac{1}{2011}$ + $\frac{1}{2011}$ – $\frac{1}{2016}$) = $\frac{1}{5}$ . ($1$ – $\frac{1}{2016}$) = $\frac{1}{5}$ . ($\frac{2016}{2016}$ – $\frac{1}{2016}$) = $\frac{1}{5}$ . $\frac{2015}{2016}$= $\frac{403}{2016}$ Bình luận
`1/1.6+1/6.11+1/11.16+…+1/2011.2016`
`=1/5(5/1.6+5/6.11+5/11.16+…+5/2011.2016)`
`=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/2011-1/2016)`
`=1/5(1-1/2016)`
`=1/5 . 2015/2016`
`=403/2016`
$\frac{1}{1.6}$ + $\frac{1}{6.11}$ + $\frac{1}{11.16}$ + $\frac{1}{16.21}$ +…+ $\frac{1}{2006.2011}$ + $\frac{1}{2011.2016}$
= $\frac{1}{5}$ . ($\frac{5}{1.6}$ + $\frac{5}{6.11}$ + $\frac{5}{11.16}$ + $\frac{5}{16.21}$ +…+ $\frac{5}{2006.2011}$ + $\frac{5}{2011.2016}$)
= $\frac{1}{5}$ . ($\frac{1}{1}$ – $\frac{1}{6}$ + $\frac{1}{6}$ – $\frac{1}{11}$ + $\frac{1}{11}$ – $\frac{1}{16}$ + $\frac{1}{16}$ – $\frac{1}{21}$ +…+ $\frac{1}{2006}$ – $\frac{1}{2011}$ + $\frac{1}{2011}$ – $\frac{1}{2016}$)
= $\frac{1}{5}$ . ($1$ – $\frac{1}{2016}$)
= $\frac{1}{5}$ . ($\frac{2016}{2016}$ – $\frac{1}{2016}$)
= $\frac{1}{5}$ . $\frac{2015}{2016}$= $\frac{403}{2016}$