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Q
16 tháng 4 2017
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)
\(=5^2\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}\right)\)
\(=25.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right)\)
\(=5\left(1-\frac{1}{26}\right)\)
\(=5.\frac{25}{26}\)
\(=\frac{125}{26}\)
27 tháng 4 2019
\(S=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}\)
\(S=\frac{25}{1\cdot6}+\frac{25}{6\cdot11}+\frac{25}{11\cdot16}+\frac{25}{16\cdot21}+\frac{25}{21\cdot26}\)
\(S=5\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}\right]\)
\(S=5\left[1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right]\)
\(S=5\left[1-\frac{1}{26}\right]=5\cdot\frac{25}{26}=\frac{125}{26}\)
27 tháng 4 2019
Bài làm
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 = \(\frac{5}{1.6}\)+ \(\frac{5}{6.11}\)+ \(\frac{5}{11.16}\) + \(\frac{5}{16.21}\) + \(\frac{5}{21.26}\)
S : 5 = 1 - \(\frac{1}{6}\)+ \(\frac{1}{6}\)- \(\frac{1}{11}\) + \(\frac{1}{11}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{21}\)+ \(\frac{1}{21}\)- \(\frac{1}{26}\)
S : 5 = 1 - \(\frac{1}{26}\)
S : 5 = \(\frac{25}{26}\)
S = \(\frac{125}{26}\)
NM
0
NB
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KT
29 tháng 6 2018
mk chỉnh lại đề nhé, có lẽ bn ghi thiếu:
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}+\frac{5^2}{31.36}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}+\frac{5}{31.36}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}\right)\)
\(=5\left(1-\frac{1}{36}\right)=5.\frac{35}{36}=\frac{175}{36}\)
HN
29 tháng 6 2018
Đề đúng:
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}+\frac{5^2}{31.36}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}+\frac{5}{31.36}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}\right)\)
\(=5\left(1-\frac{1}{36}\right)\)
\(=5\left(\frac{36}{36}-\frac{1}{36}\right)\)
\(=5.\frac{35}{36}\)
\(=\frac{175}{36}\)
21 tháng 11 2018
a) \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
=> \(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
=> \(A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)
21 tháng 11 2018
a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66
= (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)
= 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)
= 25/66
b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7
= (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)
= 1/1 - 1/7 = 6/7
c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21
C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)
C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]
C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)
C = 1
Dễ nhưng dài quá !
10 tháng 9 2019
A = 3/11x16 + 3/16x21 + 3/21x26 +...+3/61x66
A : 3 . 5 = 5/11x16 + 5/16x21 + 5/21x26 +...+5/61x66
A : 3 . 5 = 1/11 - 1/16 + 1/16 - 1/21 + ......+ 1/61 - 1/66
A : 3 . 5 = 1/11 - 1/66
A : 3 . 5 = 5/66
A = 5/66 . 3 : 5
A = 5/22 : 5
A = 1/22
Chúc bạn hoc tốt 
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)
\(5S=5^2\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}\right)\)
\(5S=5^2\left(1-\frac{1}{26}\right)\)
\(\Rightarrow S=5^2:5\left(1-\frac{1}{26}\right)\)
\(S=5\left(1-\frac{1}{26}\right)\)
\(S=5.\frac{25}{26}\)
\(S=\frac{125}{26}\)