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
Ta có :
\(M=\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...................+\dfrac{10}{1400}\)
\(M=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...............+\dfrac{5}{700}\)
\(M=\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+..............+\dfrac{5}{25.28}\)
\(\dfrac{3}{5}M=\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+............+\dfrac{1}{25}-\dfrac{1}{27}\right)\)
\(\dfrac{3}{5}M=\dfrac{1}{4}-\dfrac{1}{27}\)
\(\dfrac{3}{5}M=\dfrac{3}{14}\)
\(M=\dfrac{3}{14}:\dfrac{3}{5}=\dfrac{5}{24}\)
\(\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...+\dfrac{10}{1400}=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)
\(=\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+...+\dfrac{5}{25.28}\)
\(=\dfrac{5}{3}.\left(\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{25.28}\right)\)
\(=\dfrac{5}{3}.\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}.\left(\dfrac{1}{4}-\dfrac{1}{28}\right)=\dfrac{5}{3}.\dfrac{3}{14}=\dfrac{5}{14}\)
Chúc bạn học tốt!!!
\(\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...+\dfrac{10}{1400}=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)
=\(\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+...+\dfrac{5}{25.28}\)
\(=\dfrac{5}{3}\left(\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{25.28}\right)\)\(=\dfrac{5}{3}.\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}.\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}.\left(\dfrac{7}{28}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}.\dfrac{3}{14}=\dfrac{5}{14}\)
Chúc học tốt, đạt học sinh giỏi!!!
