N=10/50+10/140+10/260+..+10/1400
Ai biết giúp mình với.
K
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NT
1
DT
0
TV
1
6 tháng 4 2016
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
tích nha
15 tháng 3 2017
\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)
\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+......+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+......+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}\)
\(=\frac{5}{14}\)
NC
0
NT
1
4 tháng 10 2016
\(S=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+.......+\frac{10}{1400}\)
\(S=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+\frac{5}{700}\)
\(\frac{3S}{5}=\frac{3}{4}\times7+\frac{3}{7}\times10+\frac{30}{10}\times13+........+\frac{3}{25}\times28\)
\(\frac{3S}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+......+\frac{1}{25}-\frac{1}{28}\)
\(\frac{3S}{5}=\frac{1}{4}-\frac{1}{28}\)
\(\frac{3S}{5}=\frac{3}{14}\)
\(S=\frac{3}{14}\times\frac{5}{3}\)
\(S=\frac{5}{14}\)
Vậy \(S=\frac{5}{14}\)
KN
10 tháng 9 2016
\(A=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+....+\frac{10}{1400}\)
\(A=\frac{5}{28}+\frac{5}{70}+\frac{5}{135}+...+\frac{5}{700}\)
\(A=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)
\(A.\frac{3}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{13}-....+\frac{1}{25}-\frac{1}{28}\)
\(A.\frac{3}{5}=\frac{1}{4}-\frac{1}{28}=\frac{3}{14}\)
\(A=\frac{3}{14}:\frac{3}{5}=\frac{5}{14}\)
PN
2
1056+10140+10260+...+101400=528+570+5130+...+57001056+10140+10260+...+101400=528+570+5130+...+5700
=54.7+57.10+510.13+...+525.2854.7+57.10+510.13+...+525.28
=53(34.7+37.10+310.13+...+325.28)=53(34.7+37.10+310.13+...+325.28)=53.(14−17+17−110+...+125−128)=53.(14−17+17−110+...+125−128)
=53.(14−128)=53.(14−128)
=53.(728−128)=53.(728−128)
=53.314=514
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+...+1/25−1/28)
=5/3(1/4−1/28)
=5/3.3/14=5/14