D=10/56 + 10/140 + 10/260+.....+ 10/1400
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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
\(=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+...+\frac{20}{2800}=20\left(\frac{1}{8.14}+\frac{1}{14.20}+\frac{1}{20.26}+...+\frac{1}{50.56}\right)\)
\(=20\left(\frac{1}{8}-\frac{1}{56}\right)=20.\frac{3}{28}=\frac{15}{7}\)
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
SG
24 tháng 4 2016
A=10/56+10/140+10/260+...+10/1400
=\(\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
=\(\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
=\(\frac{5}{3}\)(\(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\))
=\(\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
=\(\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
=\(\frac{5}{3}.\frac{3}{14}\)
=\(\frac{5}{14}\)
TN
4
26 tháng 2 2017
\(C=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+....+\frac{10}{1400}\)
\(=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+....+\frac{5}{25.28}\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}=\frac{5}{14}\)
Ta co :
D=10/56+10/140+10/260+....+10/1400
D=5/28+5/70+5/130+....+5/700
3D/5=3/4.7+3/7.10+3/10.13+...+3/25.28
3D/5=1/4-1/7+1/7-1/10+1/10-1/13+....+1/25-1/28
3D/5=1/4-1/28 3S/5=3/14 S=3/14.5/3
D=5/14
Vay tong D=5/14