\(S=2\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)

\(S=2\left(1-\frac{1}{106}\right)\)

\(S=\frac{210}{106}=\frac{105}{53}\)

\(S=2.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)

\(S=2.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-...-\frac{1}{101}+\frac{1}{101}-\frac{1}{106}\right)\)

\(S=2.\left[1+\left(\frac{-1}{6}+\frac{1}{6}\right)+\left(\frac{-1}{11}\frac{1}{11}\right)+...+\left(\frac{-1}{101}+\frac{1}{101}\right)-\frac{1}{106}\right]\)

\(S=2.\left[1+0+0+...+0-\frac{1}{106}\right]\)

\(S=2.\left[1-\frac{1}{106}\right]\)

\(S=2.\frac{105}{106}\)

\(S=\frac{10}{1.6}+\frac{10}{6.11}+...+\frac{10}{101.106}\)

=\(2\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)

\(=2\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{101}+\frac{1}{106}\right)\)

\(=2\left(1-\frac{1}{106}\right)=2.\frac{105}{106}=\frac{105}{53}\)

Tính S:

S=5.(\(\dfrac{5}{1.6}\)+\(\dfrac{5}{6.11}\)+...+\(\dfrac{5}{101.106}\))

S=5.(1-\(\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\))

S=5.(1-\(\dfrac{1}{106}\))

S=5.\(\dfrac{105}{106}\)

S=\(\dfrac{525}{106}\)

525/106

\(S=\dfrac{10}{1.6}+\dfrac{10}{6.11}+...+\dfrac{10}{101.106}\)

\(=\dfrac{10}{5}.\left(\dfrac{1}{1.6}+\dfrac{1}{6.11}+...+\dfrac{1}{101.106}\right)\)

\(=2.\left(\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)

\(=2.\left(\dfrac{1}{1}-\dfrac{1}{106}\right)\)

\(=2.\dfrac{105}{106}\)

= \(\dfrac{2.105}{106}\)\(=\dfrac{210}{106}=\dfrac{105}{53}\)

\(A=\frac{10^2}{1\cdot6}+\frac{10^2}{6\cdot11}+...+\frac{10^2}{61\cdot66}=\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+...+\frac{5}{61\cdot66}\right)\cdot20\)

\(=\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{61}-\frac{1}{66}\right)\cdot20\)

\(=\left[\left(1-\frac{1}{66}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\cdot20\)

\(=\left[\left(\frac{66}{66}-\frac{1}{66}\right)+0+...+0\right]\cdot20=\frac{65}{66}\cdot20=\frac{65\cdot20}{66}=\frac{65\cdot10}{33}=\frac{650}{33}\)

\(A=\frac{10^2}{1.6}+\frac{10^2}{6.11}+...+\frac{10^2}{61.66}\)

\(=10^2.\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{61.66}\right)\)

\(=10^2.5.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=500.\left(1-\frac{1}{66}\right)\)

\(=500.\frac{65}{66}\)

\(=\frac{16250}{33}\)

\(.S=3.\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{96.101}\right)\)

\(\Rightarrow S=3.\frac{1}{5}\left(\frac{1}{1}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{101}\right)\)

\(\Rightarrow S=\frac{3}{5}.\left(\frac{1}{1}-\frac{1}{101}\right)\)

\(\Rightarrow S=\frac{3}{5}.\left(\frac{100}{101}\right)\)

\(S=\frac{60}{101}\)

\(\frac{100}{101}\)nha

bạn tự tính

tíc mình nha

S=3/1.6+3/6.11+3/11.16+...+3/96.101

=>S=1/1.6+1/6.11+1/11.16+...+1/96.101

S=1-1/6+1/6-1/11+1/11-1/16+...+1/96-1/101

S=1-1/101

S=100/101

\(\frac{3}{1.6}+\frac{3}{6.11}+\frac{3}{11.16}+...+\frac{3}{96.101}\)

\(=3.\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{96.101}\right)\)

\(=\frac{3}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{96}-\frac{1}{101}\right)\)

\(=\frac{3}{5}.\left(1-\frac{1}{101}\right)\)

\(=\frac{3}{5}.\frac{100}{101}\)

\(=\frac{60}{101}\)

đm dễ thế này thi tự làm đi hỏi cc

 = 2.(5/1.6+5/6.11+.....+5/56.61)

 = 2.(1-1/6+1/6-1/11+.....+1/56-1/61)

 = 2.(1-1/61)

 = 2.60/61 = 120/61

Tk mk nha

\(\frac{10}{1.6}+\frac{10}{6.11}+...+\frac{10}{56.61}\)

\(=10.\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{56.61}\right)\)

\(=10.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{56}-\frac{1}{61}\right)\)

\(=2\left(1-\frac{1}{61}\right)\)

\(=2.\frac{60}{61}\)

\(=\frac{120}{61}\)

\(S=\frac{10}{2.4}+\frac{10}{4.6}+...+\frac{10}{2008.2010}\)

\(S=5\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2008.2010}\right)\)

\(S=5\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(S=5\left(\frac{1}{2}-\frac{1}{2010}\right)=5.\frac{502}{1005}=\frac{502}{201}\)

S=\(\frac{10}{2}-\frac{10}{4}+\frac{10}{4}-\frac{10}{6}+....\frac{10}{2008}-\frac{10}{2010}\)

S=\(\frac{10}{2}-\frac{10}{2010}=5-\frac{1}{201}=\frac{5}{1}-\frac{1}{201}=\frac{1005}{201}-\frac{1}{201}=\frac{1004}{201}\)

\(=5\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(=5\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(=5.\frac{1004}{2010}\)

\(=\frac{1004}{402}=\frac{502}{201}\)

S = 10/56 + 10/140 + 10/260 + ....... + 10/1400

S = 5/28 + 5/70 + 5/130 + 5/700

3S/5 = 3/4 x 7 + 3/7 x 10 + 30/10 x 13 + ....... + 3/25 x 28

3S/5 = 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ........ + 1/25 - 1/28

3S/5 = 1/4 - 1/28

3S/5 = 3/14

S = 3/14 x 5/3

S = 5/14

Vậy S = 5/14

\(S=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\frac{10}{1400}\)

\(S=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(S=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)

\(S=5.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)

\(S=5.\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)

\(S=5.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(S=5.\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(S=5.\frac{3}{14}=\frac{15}{14}\)

Vậy \(S=\frac{15}{14}\)

thank 2 bạn nha!