Rút gọn rồi tách mẫu là đ

\(A=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)

\(\dfrac{3A}{5}=\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{25.28}\)

\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\)

\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{28}=\dfrac{3}{14}\)

⇒ \(A=\dfrac{5}{14}\)

\(=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+...+\frac{20}{2800}=20\left(\frac{1}{8.14}+\frac{1}{14.20}+\frac{1}{20.26}+...+\frac{1}{50.56}\right)\)

\(=20\left(\frac{1}{8}-\frac{1}{56}\right)=20.\frac{3}{28}=\frac{15}{7}\)

Sửa đề: \(M=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\cdots+\frac{10}{1400}\)

Ta có: \(M=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\cdots+\frac{10}{1400}\)

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

\(=\frac{5}{4\cdot7}+\frac{5}{7\cdot10}+\frac{5}{10\cdot13}+\cdots+\frac{5}{25\cdot28}\)

\(=\frac53\left(\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\cdots+\frac{3}{25\cdot28}\right)\)

\(=\frac53\left(\frac14-\frac17+\frac17-\frac{1}{10}+\cdots+\frac{1}{25}-\frac{1}{28}\right)\)

\(=\frac53\left(\frac14-\frac{1}{28}\right)=\frac53\cdot\frac{6}{28}=\frac53\cdot\frac{3}{14}=\frac{5}{14}\)

\(\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+\frac{5}{208}+\frac{5}{304}=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\right)\)

\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{16}-\frac{1}{19}\right)=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{19}\right)\)

\(=\frac{5}{3}.\frac{15}{74}=\frac{25}{74}\)

gọi bt trên là A

ta có 3/10A=6/112+6/280+.........+6/2800

                 =6/8*14+6/14*20+.....+6/50*56

                 =1/8-1/14+1/14-1/20+........+1/50-1/56

                 =1/8-1/56=3/28

suy ra A=3/28*10/3=5/14

tích hộ nha

5/14 nha

HT

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