A=5/3+5/15+5/35+5/63+...+5/255=?
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AN
2
30 tháng 8 2015
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=\frac{5}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{11\cdot13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\frac{12}{13}\)
\(=\frac{30}{13}\)
30 tháng 8 2015
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)
\(=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}.\frac{12}{13}\)
\(=\frac{30}{13}\)
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
\(A=\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+...+\frac{5}{399}\)
\(A=\frac{5}{3.5}+\frac{5}{5.7}+\frac{5}{7.9}+...+\frac{5}{19.21}\)
\(2A=5\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)\)
\(2A=5\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(2A=5\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(2A=5.\frac{2}{7}\)
\(2A=\frac{10}{7}\)
\(\Rightarrow A=\frac{5}{7}\)
KL
6
8 tháng 6 2017
Ta có:
\(A=\frac{5}{15}+...+\frac{5}{399}\)
\(\Rightarrow A=5.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\right)\)
\(\Rightarrow A=\frac{5}{2}.\left(\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(\Rightarrow A=\frac{5}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(\Rightarrow A=\frac{5}{7}\)
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!
PV
11 tháng 4 2016
a) A x 3/5 = 3/1.4 + 3/4.7 + 3/7.10 + ...+ 3/100.103
= 1 - 1/4 + 1/4 - 1/7 + 1/7 -1/10 + ... + 1/100 - 1/103
= 1 - 1/103
= 102/103 => A = 102/103 : 3/5 = 170/103
b) B = 1/3.5 + 1/5.7 + 1/7.9 + ...+ 1/49.51
B x2 = 2/3.5 + 2/5.7 + 2/7.9 + ...+ 2/49.51
= 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ...+ 1.49 - 1/51
= 1/3 - 1/51
= 16/51
=> B = 16/51 : 2 = 8/51
\(\frac{35}{51}\)