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N
25 tháng 3 2019
\(S=2\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)
\(S=2\left(1-\frac{1}{106}\right)\)
\(S=\frac{210}{106}=\frac{105}{53}\)
TN
26 tháng 3 2019
\(S=2.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{101.106}\right)\)
\(S=2.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-...-\frac{1}{101}+\frac{1}{101}-\frac{1}{106}\right)\)
\(S=2.\left[1+\left(\frac{-1}{6}+\frac{1}{6}\right)+\left(\frac{-1}{11}\frac{1}{11}\right)+...+\left(\frac{-1}{101}+\frac{1}{101}\right)-\frac{1}{106}\right]\)
\(S=2.\left[1+0+0+...+0-\frac{1}{106}\right]\)
\(S=2.\left[1-\frac{1}{106}\right]\)
\(S=2.\frac{105}{106}\)
8 tháng 7 2017
\(A=\frac{20}{1\cdot6}+\frac{20}{6\cdot11}+...+\frac{20}{51\cdot56}+\frac{20}{56\cdot61}\)
\(A=\frac{20}{5}\cdot\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{51}-\frac{1}{56}+\frac{1}{56}-\frac{1}{61}\right)\)
\(A=4\cdot\left(1-\frac{1}{61}\right)\)
\(A=4\cdot\frac{60}{61}\)
\(A=\frac{240}{61}\)
DP
8 tháng 7 2017
\(A=\frac{20}{1.6}+\frac{20}{6.11}+...+\frac{20}{51.56}+\frac{20}{56.61}\)
\(A=\frac{20}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{51}-\frac{1}{56}+\frac{1}{56}-\frac{1}{61}\right)\)
\(A=4.\left(1-\frac{1}{61}\right)\)
\(A=4.\frac{60}{61}=\frac{240}{61}\)
19 tháng 4 2016
S = 2(5/1.6 + 5/6.11 +.......+ 5/101.106)
S = 2( 1 - 1/6 + 1/6 - 1/11 +.....+ 1/101 - 1/106)
S = 2( 1 - 1/106)
S = 2 . 105/106
S = 105/53
k mk đi,mk mới bị trừ điểm!
19 tháng 4 2016
1/2.S=5/(1.6)+5/(6.11)+...+5/(101.106)
1/2.S=1/1-1/6+1/6-1/11+...+1/101-1/106
1/2.S=1/1-1/106
1/2.S=105/106
S=105/53
11 tháng 5 2019
\(=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
\(=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5.\left(1-\frac{1}{31}\right)\)
\(=5.\frac{30}{31}\)
\(=\frac{6}{31}\)
11 tháng 5 2019
\(=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}\right)\)
\(=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5.\left(1-\frac{1}{31}\right)=\frac{150}{31}\)
16 tháng 4 2018
Ta có :
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)
\(S=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)
\(S=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)
\(S=5\left(1-\frac{1}{26}\right)\)
\(S=5.\frac{25}{26}\)
\(S=\frac{125}{26}\)
Vậy \(S=\frac{125}{26}\)
Chúc bạn học tốt ~
16 tháng 4 2018
\(S=\frac{5^2}{1\cdot6}\cdot\frac{5^2}{6\cdot11}\cdot\frac{5^2}{11\cdot16}\cdot\frac{5^2}{16\cdot21}\cdot\frac{5^2}{21\cdot26}\)
\(=5\cdot\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}\right)\)
\(=5\cdot\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)
\(=5\cdot\left(1-\frac{1}{26}\right)\)
\(=5\cdot\frac{25}{26}\)
\(=\frac{125}{26}\)
19 tháng 3 2017
ta co \(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}\)
=\(5.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}\right)\)
=\(5.\left(\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}+\frac{26-21}{21.26}+\frac{31-26}{26.31}\right)\)
=\(5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}\right)\)
=\(5.\left(1-\frac{1}{31}\right)\)
=\(5.\frac{30}{31}\)
=\(\frac{150}{31}\)
1 tháng 8 2017
Ta có : \(\frac{5.5}{1.6}+\frac{5.5}{6.11}+\frac{5.5}{11.16}+\frac{5.5}{16.21}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}\right)\)
\(=5\left(1-\frac{1}{21}\right)\)
\(=5.\frac{20}{21}=\frac{100}{21}\)
T
22 tháng 7 2019
#)Giải :
Ta có :
\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}=5\left(\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)=5\left(1-\frac{1}{31}\right)=5\times\frac{30}{31}=\frac{150}{31}>1\)
\(\Rightarrow A>1\)
9 tháng 5 2019
\(B=\frac{10}{3\cdot8}+\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+\frac{10}{23\cdot28}\)
\(B=2\left[\frac{5}{3\cdot8}+\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+\frac{5}{23\cdot28}\right]\)
\(B=2\left[\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...+\frac{1}{23}-\frac{1}{28}\right]\)
\(B=2\left[\frac{1}{3}-\frac{1}{28}\right]=\frac{25}{42}\)
= 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
\(\frac{10}{1.6}+\frac{10}{6.11}+...+\frac{10}{56.61}\)
\(=10.\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{56.61}\right)\)
\(=10.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{56}-\frac{1}{61}\right)\)
\(=2\left(1-\frac{1}{61}\right)\)
\(=2.\frac{60}{61}\)
\(=\frac{120}{61}\)