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22 tháng 2 2023
1: \(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
=1/2*10/39
=5/39
2: \(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)=\dfrac{5}{2}\cdot\dfrac{10}{11}=\dfrac{50}{22}=\dfrac{25}{11}\)
25 tháng 7 2019
Đặt \(A=\)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
\(2A=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)
\(A=\frac{5}{39}\)
Câu còn lại cx dựa như vậy nhé bn !
Chúc bn hc tốt <3
S
15 tháng 4 2019
\(\frac{3x}{5}=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)
Ta có: \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{13}\right)\)
\(=\frac{1}{2}.\frac{12}{13}\)
\(=\frac{6}{13}\)
\(\frac{3x}{5}=\frac{6}{13}\)
\(\Rightarrow3x=\frac{6.5}{13}\)
\(\Rightarrow3x=\frac{30}{13}\)
\(\Rightarrow x=\frac{10}{13}\)
~Học tốt~
DT
22 tháng 4 2016
Ta có:
A=5/15+5/35+5/63+5/99+...+5/2915
=>A=5/3.5+5/5.7+5/7.9+5/9.11+...+5/53.55
=>A=5/2.(2/3.5+2/5.7+2/7.9+2/9.11+...+2/53.55)
=>A=5/2.(2/3-2/5+2/5-2/7+2/7-2/9+2/9-2/11+...+2/53-2/55)
=>A=5/2.(2/3-2/55)
=>A=5/2.104/165
=>A=52/33
Vậy A=52/33
OK!
DP
30 tháng 6 2017
\(X-\left(\frac{31}{5}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)
\(X-\left(\frac{31}{5}+\frac{31}{3\cdot5}+\frac{31}{5\cdot7}+\frac{31}{7\cdot9}+\frac{31}{9\cdot11}+\frac{31}{11\cdot13}\right)=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\left[\frac{31}{2}\cdot\frac{10}{39}+\frac{31}{5}\right]=\frac{9}{13}\)
\(X-\frac{1984}{195}=\frac{9}{13}\)
\(\Rightarrow X=\frac{9}{13}+\frac{1984}{195}=\frac{163}{15}\)
11 tháng 5 2017
\(A=\frac{5}{3\cdot5}+\frac{5}{5\cdot7}+\frac{5}{7\cdot9}+......+\frac{5}{19\cdot21}\)
\(A=\frac{5}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{19}-\frac{1}{21}\right)\)
\(A=\frac{5}{2}\left(\frac{1}{3}-\frac{1}{21}\right)\)
còn lại tự tính nha
ok xong r đó
Q
11 tháng 5 2017
\(A=\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+...+\frac{5}{399}\)
\(A=\frac{5}{3.5}+\frac{5}{5.7}+\frac{5}{7.9}+...+\frac{5}{19.21}\)
\(2A=5\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)\)
\(2A=5\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(2A=5\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(2A=5.\frac{2}{7}\)
\(2A=\frac{10}{7}\)
\(\Rightarrow A=\frac{5}{7}\)
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=\frac{5}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{11\cdot13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\frac{12}{13}\)
\(=\frac{30}{13}\)
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)
\(=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}.\frac{12}{13}\)
\(=\frac{30}{13}\)