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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

25 tháng 4 2017

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)

\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)

\(2A=1-\frac{1}{3^{100}}\)

\(A=\frac{1-\frac{1}{3^{100}}}{2}\)

\(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)

\(3B=\frac{5.3}{4.7}+\frac{5.3}{7.10}+\frac{5.3}{10.13}+...+\frac{5.3}{25.28}\)

\(3B=5\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)

\(3B=5\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(3B=5\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(3B=5\cdot\frac{3}{14}=\frac{15}{14}\)

\(B=\frac{15}{14}:3=\frac{5}{14}\)

25 tháng 4 2017

a) \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)

\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)

\(2A=1-\frac{1}{3^{100}}\)

\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)

b)  \(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)

\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{5}{3}.\left(\frac{1}{7}-\frac{1}{10}\right)+\frac{5}{3}.\left(\frac{1}{10}-\frac{1}{13}\right)+...+\frac{5}{3}.\left(\frac{1}{25}-\frac{1}{28}\right)\)

\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(B=\frac{5}{3}.\frac{3}{14}\)

\(\Rightarrow B=\frac{5}{14}\)

15 tháng 3 2017

\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)

\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)

\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+......+\frac{3}{25.28}\right)\)

\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+......+\frac{1}{25}-\frac{1}{28}\right)\)

\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(=\frac{5}{3}.\frac{3}{14}\)

\(=\frac{5}{14}\)

17 tháng 1 2016

M=5/28+5/70+...+5/700=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

6 tháng 3 2016

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 :D 

13 tháng 4 2016

Doãn Hải Anh mk lớp 7 nên quên òi 

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

\(C=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}=10\left(\frac{1}{56}+\frac{1}{140}+\frac{1}{260}+...+\frac{10}{1400}\right)\)

\(C=\frac{10}{2}\left(\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+...+\frac{1}{700}\right)=5\left(\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+\frac{1}{10\cdot13}+...+\frac{1}{25\cdot28}\right)\)

\(C=5\cdot\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(C=\frac{5}{3}\cdot\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}\cdot\frac{3}{14}=\frac{5}{14}\)

15 tháng 3 2017

Vừa nãy mk k cho bạn đấy,Lê Mai Uyên ạ!

15 tháng 3 2017

đáp số là 5/14