Tính tổng : \(R=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
Ai nhanh nhất mình sẽ tick cho ^_^ nhớ kb với mình nhé
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NM
4
9 tháng 8 2016
S = 10/56 + 10/140 + 10/260 + ....... + 10/1400
S = 5/28 + 5/70 + 5/130 + 5/700
3S/5 = 3/4 x 7 + 3/7 x 10 + 30/10 x 13 + ....... + 3/25 x 28
3S/5 = 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ........ + 1/25 - 1/28
3S/5 = 1/4 - 1/28
3S/5 = 3/14
S = 3/14 x 5/3
S = 5/14
Vậy S = 5/14
9 tháng 8 2016
\(S=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\frac{10}{1400}\)
\(S=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(S=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(S=5.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
\(S=5.\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)
\(S=5.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(S=5.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(S=5.\frac{3}{14}=\frac{15}{14}\)
Vậy \(S=\frac{15}{14}\)
US
0
CA
1
ND
1
18 tháng 6 2016
\(\frac{10}{56}+\frac{10}{140}+...+\frac{10}{1400}\)
\(=\frac{5}{28}+\frac{5}{70}+...+\frac{5}{700}\)
\(=\frac{5}{3}\left(\frac{3}{28}+\frac{3}{70}+...+\frac{3}{700}\right)\)
\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}=\frac{5}{14}\)
HN
3
TN
25 tháng 4 2016
\(=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\times\frac{3}{14}\)
\(=\frac{5}{14}\)
HT
19 tháng 3 2016
A = 10/56 + 10/140 + 10/260 + .......+ 10/1400
A = 5/28 + 5/70 + 5/130 +.........+ 5/700
3A/5 = 3/4.7 + 3/7.10 + 3/10.13 +.......+ 3/25.28
3A/5 = 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 +........+ 1/25 - 1/28
3A/5 = 1/4 - 1/28
3A/5 = 3/14
A = 3/14 . 5/3
A = 5/14
Vậy A = 5/14
19 tháng 3 2016
A= 5/3.(3/28+3/70+3/130+...+3/700) A=5/3.(3/4.7+3/7.10+3/10.13+...+3/25.28)
A=5/3.(1/4-1/7+1/7-1/10+1/10-1/13+...+1/25-1/28)
A=5/3(1/4-1/28)
A=5/3.(7/28-1/28)
A=5/3.3/14
A=5/14
3 tháng 4 2016
S = 5/28 + 5/70 + 5/130 + ..... + 5/700
S = 5 / 4x7 + 5 / 7x10 + 5 / 10x13 + ..... + 5 / 25x28
SX3 / 5 = 3 / 4x7 + 3 / 7x10 + ....... + 3 / 25x28
Sx3/5=1/4-1/7+1/7-1/10+1/10+.....+1/25-1/28
Sx3/5=1/4+(1/7-1/7)+(1/9-1/9)+.....+(!/25-1/25)-1/28
Sx3/5=1/4-1/28
Sx3/5=3/14
S = 3/14: 3/5
S = 5/14
Vậy S = 5 /14
tk mk nhé !
3 tháng 4 2016
\(C=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}=10\left(\frac{1}{56}+\frac{1}{140}+\frac{1}{260}+...+\frac{10}{1400}\right)\)
\(C=\frac{10}{2}\left(\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+...+\frac{1}{700}\right)=5\left(\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+\frac{1}{10\cdot13}+...+\frac{1}{25\cdot28}\right)\)
\(C=5\cdot\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(C=\frac{5}{3}\cdot\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}\cdot\frac{3}{14}=\frac{5}{14}\)
\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)
\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+......+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+......+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}\)
\(=\frac{5}{14}\)