S=10/56+10/140+10/260+....10/1400
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15 tháng 3 2017
\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)
\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+......+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+......+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}\)
\(=\frac{5}{14}\)
PN
15
12 tháng 4 2015
S=10/56+10/140+10/260+....+10/1400
S=5/28+5/70+5/130+....+5/700
3S/5=3/4.7+3/7.10+3/10.13+...+3/25.28
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=3/14.5/3
S=5/14
Vậy S=5/14
16 tháng 4 2015
S=10/56+10/140+10/260+...........+10/1400
S=5/28+5/70+5/130+........+5/700
3S/5=3/4.7+3/7.10+3/13.10+.........+3/25.28
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=3/14.5/3
S=5/14
PM
1
5 tháng 3 2017
\(H=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(\Rightarrow H=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(\Rightarrow\frac{3H}{5}=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\)
\(\Rightarrow\frac{3H}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)
\(\Rightarrow\frac{3H}{5}=\frac{1}{4}-\frac{1}{28}\)
\(\Rightarrow\frac{3H}{5}=\frac{3}{14}\)
\(\Rightarrow H=\frac{3}{14}.\frac{5}{3}\)
\(\Rightarrow H=\frac{5}{14}\)
Vậy \(H=\frac{5}{14}\)
LB
25 tháng 3 2017
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\\ A=\frac{1}{75}\)
\(B=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146+150}=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{94}+\frac{15}{94}-\frac{15}{98}+...+\frac{15}{146}-\frac{15}{150}\right)\)
\(B=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{150}\right)=\frac{1}{60}\)
25 tháng 4 2016
10/56+10/140+10/260 +....+10/1400
=5/28+5/70+5/130+...+5/700
=5/4.7+5/7.10+5/10.13+...+5/25.28
=5/3(1/4-1/7+1/7-1/10+1/10-1/13+.....+1/25-1/28)
=5/3(1/4-1/28)
=5/3.3/14
=5/14
TT
7 tháng 5 2017
@Thành Tò Văn
Đầu tiên rút gọn M trước
M= 5/28 + 5/70 +.....+10/700
= 5/(4.7)+5/(7.10)+....5/(25.28)
3M= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28)
3M= 5 (1/4-1/28)
3M=15/14
M= 5/14
7 tháng 5 2017
Ta có :
\(M=\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...................+\dfrac{10}{1400}\)
\(M=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...............+\dfrac{5}{700}\)
\(M=\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+..............+\dfrac{5}{25.28}\)
\(\dfrac{3}{5}M=\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+............+\dfrac{1}{25}-\dfrac{1}{27}\right)\)
\(\dfrac{3}{5}M=\dfrac{1}{4}-\dfrac{1}{27}\)
\(\dfrac{3}{5}M=\dfrac{3}{14}\)
\(M=\dfrac{3}{14}:\dfrac{3}{5}=\dfrac{5}{24}\)
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 \(S=\frac{15}{14}\)
DQ
1
26 tháng 2 2019
H=10/56+10/140+10/260+....+10/1400
H=5/28+5/70+5/130+....+5/700
3H/5=3/4.7+3/7.10+3/10.13+...+3/25.28
3H/5=1/4-1/7+1/7-1/10+1/10-1/13+....+1/25-1/28
3H/5=1/4-1/28
3H/5=3/14
H=3/14.5/3
H=5/14
Vậy H=5/14
Đầu tiên rút gọn S trước
S= 5/28 + 5/70 +.....+10/700
= 5/(4.7)+5/(7.10)+....5/(25.28)
3S= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28)
3S= 5 (1/4-1/28)
3S=15/14
S= 5/14
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