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NM
0
TK
3
10 tháng 4 2018
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(\frac{5^2}{1.6}=5.\left(\frac{1}{1}-\frac{1}{6}\right)\)
\(\frac{5^2}{6.11}=5.\left(\frac{1}{6}-\frac{1}{11}\right)\)
............................
\(\frac{5^2}{26.31}=5.\left(\frac{1}{26}-\frac{1}{31}\right)\)
cộng hết lại: \(5.\left(\frac{1}{1}-\frac{1}{31}\right)=5\left(\frac{30}{31}\right)=\frac{150}{31}\)
10 tháng 4 2018
Ta có :
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)
\(=\)\(5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)
\(=\)\(5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=\)\(5\left(1-\frac{1}{31}\right)\)
\(=\)\(5-\frac{5}{31}\)
\(=\)\(\frac{150}{31}\)
Chúc bạn học tốt ~
V
2
17 tháng 9 2016
\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{1}{26.31}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)
\(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{31-1}{31}\)
\(=\frac{30}{31}\)
Vậy \(A=\frac{30}{31}\)
17 tháng 9 2016
\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)
\(\Rightarrow A=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)
\(\Rightarrow A=\frac{1}{1}-\frac{1}{31}\)
\(\Rightarrow A=\frac{30}{31}\)
IW
8 tháng 7 2016
\(\Rightarrow A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+.....+\frac{1}{26}-\frac{1}{31}\)
\(\Rightarrow A=1-\frac{1}{31}\)
\(\Rightarrow A=\frac{30}{31}\)
MH
8 tháng 7 2016
\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)
\(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{31-1}{31}=\frac{30}{31}\)
\(\text{Vậy }A=\frac{30}{31}\).
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:
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}+\frac{5^2}{31.36}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}+\frac{5}{31.36}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}\right)\)
\(=5\left(1-\frac{1}{36}\right)\)
\(=5\left(\frac{36}{36}-\frac{1}{36}\right)\)
\(=5.\frac{35}{36}\)
\(=\frac{175}{36}\)
Q
16 tháng 4 2017
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)
\(=5^2\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}\right)\)
\(=25.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right)\)
\(=5\left(1-\frac{1}{26}\right)\)
\(=5.\frac{25}{26}\)
\(=\frac{125}{26}\)
NB
0
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
\(=5\left(\frac{6-1}{1.6}+\frac{11-6}{6.11}+...+\frac{31-26}{26.31}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5\left(1-\frac{1}{31}\right)=\frac{150}{31}\)