10/56 + 10/140 + 10/260 + ........ + 10/1100
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TN
1
MH
25 tháng 1 2022
\(A=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)
\(\dfrac{3A}{5}=\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{25.28}\)
\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\)
\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{28}=\dfrac{3}{14}\)
⇒ \(A=\dfrac{5}{14}\)
10 tháng 4 2016
\(=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+...+\frac{20}{2800}=20\left(\frac{1}{8.14}+\frac{1}{14.20}+\frac{1}{20.26}+...+\frac{1}{50.56}\right)\)
\(=20\left(\frac{1}{8}-\frac{1}{56}\right)=20.\frac{3}{28}=\frac{15}{7}\)
ND
0
NT
1
20 tháng 4 2015
\(\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+\frac{5}{208}+\frac{5}{304}=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{16}-\frac{1}{19}\right)=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{19}\right)\)
\(=\frac{5}{3}.\frac{15}{74}=\frac{25}{74}\)
BK
18 tháng 3 2016
gọi bt trên là A
ta có 3/10A=6/112+6/280+.........+6/2800
=6/8*14+6/14*20+.....+6/50*56
=1/8-1/14+1/14-1/20+........+1/50-1/56
=1/8-1/56=3/28
suy ra A=3/28*10/3=5/14
tích hộ nha
\(\)\(\dfrac{10}{56}+\dfrac{10}{140}+...+\dfrac{10}{1400}\)
\(=\dfrac{5}{28}+\dfrac{5}{70}+...+\dfrac{5}{700}\)
\(=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}\cdot\dfrac{6}{28}=2\cdot\dfrac{5}{28}=\dfrac{10}{28}=\dfrac{5}{14}\)
\(=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\\ =\dfrac{5}{3}\left(\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+...+\dfrac{3}{25\cdot28}\right)\\ =\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\\ =\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{28}\right)=\dfrac{5}{3}\cdot\dfrac{3}{14}=\dfrac{5}{14}\)