B = 10/56 + 10/140 + 10/260 + ...+ 10/1400      

B= 5/28 + 5/70 +.....+10/700 
= 5/(4.7)+5/(7.10)+....5/(25.28) 
3B= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28) 
3B = 5 (1/4-1/28) 
3B=15/14 
B = 15/14 : 3 

B = 5/14

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

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

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

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

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

\(S=5.\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)

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

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

\(S=5.\frac{3}{14}=\frac{15}{14}\)

Vậy \(S=\frac{15}{14}\)

thank 2 bạn nha!

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

       =\(\frac{5}{3}\times\left(\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+...+\frac{3}{700}\right)\)  

      =\(\frac{5}{3}\times\left(\frac{3}{4\times7}+\frac{3}{7\times10}+\frac{3}{10\times13}+...+\frac{3}{25\times28}\right)\)  

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

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

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

      =\(\frac{5}{14}\)

Ko bít có đúng ko nhưng cứ thử nhé

M = 10/56+10/140+10/260+10/1400

M= 5/28+5/70+5/130+5/700

3M/5=1/4-1/7+1/7-1/10+1/10-1/13+...+1/25

3M/5 = 3/14

M= 3/14+5/3=5/14

Mình ghi nhầm

Giúp tôi giải toán - Hỏi đáp, thảo luận về toán học - Học toán với OnlineMath

\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{25.28}\right)=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)

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