\(\dfrac{7}{11.16}+\dfrac{7}{16.21}+\dfrac{7}{21.26}+.....+\dfrac{7}{61.66}\)
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FT
14 tháng 11 2017
\(B=\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{61.66}\)
\(B=\dfrac{5}{5}\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)
\(B=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)
\(B=\dfrac{1}{11}-\dfrac{1}{66}\)
\(B=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)
6 tháng 4 2021
\(\dfrac{5x}{1.6}+\dfrac{5x}{6.11}+\dfrac{5x}{11.16}+\dfrac{5x}{16.21}+\dfrac{5x}{21.26}+\dfrac{5x}{26.31}=1\)
\(=x\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+\dfrac{5}{16.21}+\dfrac{5}{21.26}+\dfrac{5}{26.31}\right)=1\)
\(=x\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\right)=1\)
\(=x\left(1-\dfrac{1}{31}\right)=1\)
\(\Rightarrow x=1:\left(1-\dfrac{1}{31}\right)=\dfrac{31}{30}\)
2 tháng 5 2021
Giải:
a) S=52/1.6+52/6.11+52/11.16+52/16.21+52/21.26
S=5.(5.1/6+5/6.11+5/11.16+5/16.21+5/21.26)
S=5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26)
S=5.(1/1-1/26)
S=5.25/26
S=125/26
b) (1-1/2).(1-1/3).(1-1/4).(1-1/5).....(1-1/19).(1-1/20)
=1/2.2/3.3/4.4/5.....18/19.19/20
=1.2.3.4.....18.19/2.3.4.5.....19.20
=1/20
Chúc bạn học tốt!
DH
21 tháng 11 2018
a) \(A=\dfrac{5^2}{11.16}+\dfrac{5^2}{16.21}+\dfrac{5^2}{21.26}+...+\dfrac{5^2}{56.61}\)
\(A=5^2.\left(\dfrac{1}{11.16}+\dfrac{1}{16.21}+\dfrac{1}{21.26}+...+\dfrac{1}{56.61}\right)\)
\(A=\left(5^2:5\right).\left(\dfrac{5}{11.16}+\dfrac{5}{16.21}+\dfrac{5}{21.26}+...+\dfrac{5}{56.61}\right)\)
\(A=5.\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+...+\dfrac{1}{56}-\dfrac{1}{61}\right)\)
\(A=5.\left(\dfrac{1}{11}-\dfrac{1}{61}\right)\)
\(A=5.\dfrac{50}{671}\)
\(Á=\dfrac{250}{671}\)
22 tháng 11 2022
b: \(=-2\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{2450}\right)\)
\(=-2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(=-2\cdot\dfrac{49}{50}=-\dfrac{49}{25}\)
NT
5
8 tháng 11 2019
\(A=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
8 tháng 11 2019
\(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
\(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
\(A=\frac{1}{11}-\frac{1}{66}\)
\(A=\frac{6}{66}-\frac{1}{66}\)
\(A=\frac{5}{66}\)
K
25 tháng 3 2018
a) \(\left(\dfrac{11}{12}+\dfrac{11}{12.23}+\dfrac{11}{23.34}+...+\dfrac{11}{89.100}\right)+x=\dfrac{5}{3}\)
\(\Rightarrow\left(\dfrac{11}{1.12}+\dfrac{11}{12.23}+\dfrac{11}{23.34}+...+\dfrac{11}{89.100}\right)+x=\dfrac{5}{3}\)
\(\Rightarrow\left(1-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{34}+...+\dfrac{1}{89}-\dfrac{1}{100}\right)+x=\dfrac{5}{3}\)
\(\Rightarrow1-\dfrac{1}{100}+x=\dfrac{5}{3}\)
\(\Rightarrow x=\dfrac{5}{3}-1+\dfrac{1}{100}\)
\(\Rightarrow x=\dfrac{500}{300}-\dfrac{300}{300}+\dfrac{3}{300}\)
\(\Rightarrow x=\dfrac{203}{300}\)
b) \(\left(\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{19.24}\right)-x+\dfrac{1}{3}=\dfrac{7}{3}\)
=>\(\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{19}-\dfrac{1}{24}\right)-x=\dfrac{7}{3}-\dfrac{1}{3}\)
\(\Rightarrow\dfrac{1}{11}-\dfrac{1}{24}-x=2\)
\(\Rightarrow-x=2-\dfrac{1}{11}+\dfrac{1}{24}\)
\(\Rightarrow-x=\dfrac{528}{264}-\dfrac{24}{264}+\dfrac{11}{264}\)
\(\Rightarrow x=\dfrac{515}{264}\)
c) Câu hỏi của Đàm Chu Hữu An - Toán lớp 6 - Học toán với OnlineMath
PH
7
MT
23 tháng 6 2015
\(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\)
=\(\frac{1}{5}.\frac{5}{11.16}+\frac{1}{5}.\frac{5}{16.21}+\frac{1}{5}.\frac{5}{21.26}+...+\frac{1}{5}.\frac{5}{61.66}\)
=\(\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)
=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)
=\(\frac{1}{5}.\left(\frac{6}{66}-\frac{1}{66}\right)=\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)
23 tháng 6 2015
Đặt A = \(\frac{1}{11.16}+...+\frac{1}{61.66}\)
5A = \(\frac{5}{11.16}+..+\frac{5}{61.66}\)
5a = \(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
5a = \(\frac{1}{11}-\frac{1}{61}\)
5a = 50/671
a = \(\frac{50}{671}:5=\frac{10}{671}\)
11 tháng 3 2020
\(D=\frac{3}{11\cdot16}+\frac{3}{16\cdot21}+\frac{3}{21\cdot26}+....+\frac{3}{61\cdot66}\)
\(\frac{5}{3}D=\frac{5}{3}\left(\frac{3}{11\cdot16}+\frac{3}{16\cdot21}+\frac{3}{21\cdot26}+.....+\frac{3}{61\cdot66}\right)\)
\(\frac{5}{3}D=\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}+....+\frac{5}{61\cdot66}\)
\(\frac{5}{3}D=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\)
\(\frac{5}{3}D=\frac{1}{11}-\frac{1}{66}\)
\(\frac{5}{3}D=\frac{5}{66}\)
\(D=\frac{5}{66}:\frac{5}{3}=\frac{5}{66}\cdot\frac{6}{5}=\frac{1}{11}\)
E
11 tháng 3 2020
D = 3/11.16 + 3/16.21 + 3/21.26 + ...... + 3/61.66
D = \(\frac{3}{5}\) . ( \(\frac{5}{11.16}\)+ \(\frac{5}{16.21}\)+......+\(\frac{5}{61.66}\) )
D = \(\frac{3}{5}\). ( \(\frac{1}{11}\)- \(\frac{1}{16}\) + \(\frac{1}{16}\)- \(\frac{1}{21}\)+ ......... + \(\frac{1}{61}\)- \(\frac{1}{66}\))
D =\(\frac{3}{5}\). ( \(\frac{1}{11}\)- \(\frac{1}{66}\))
D = \(\frac{3}{5}\). \(\frac{5}{66}\)
D = \(\frac{1}{22}\)
# HOK TỐT #
29 tháng 6 2022
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{29}\)
=1-1/29
=28/29
Đặt:
\(A=\dfrac{7}{11\cdot16}+\dfrac{7}{16\cdot21}+\dfrac{7}{21\cdot26}+...+\dfrac{7}{61\cdot66}\)
\(\dfrac{5}{7}A=\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{61\cdot66}\)
\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)
\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{66}=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)
\(A=\dfrac{5}{66}\cdot\dfrac{7}{5}=\dfrac{7}{66}\)