1.

A= 5/28 + 5/70 +.....+10/700 = 5/(4.7)+5/(7.10)+....5/(25.28) 

3A= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28) 

3A= 5 (1/4-1/28) 

3A=15/14 

A= 5/14 

#)Giải :

1. \(A=\frac{10}{54}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

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

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

\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)

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

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

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

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

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

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

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

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

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

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

~ Hok tốt ~

#)Next :

2. \(A=\left(\frac{1}{2^2-1}\right).\left(\frac{1}{3^2-1}\right).\left(\frac{1}{4^2-1}\right).....\left(\frac{1}{100^2-1}\right)\)

\(A=\left(-\frac{3}{2^2}\right)\left(-\frac{8}{3^2}\right).\left(-\frac{15}{4^2}\right).....\left(-\frac{9999}{100^2}\right)\)

\(A=-\left(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.....\frac{9999}{100^2}\right)\)

\(A=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\right)\)

\(A=-\left(\frac{1.2.3.....99}{2.3.4.....100}.\frac{3.4.5.....101}{2.3.4.....100}\right)\)

\(A=-\left(\frac{1}{100}.\frac{101}{2}\right)\)

\(A=-\frac{101}{200}\)

                #~Will~be~Pens~#

1)

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

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

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

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

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

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

    = \(\frac{5}{3}.\frac{3}{14}\)

    = \(\frac{5}{14}\)

#)Next : 

3. \(B=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{26.27.28.29}\)

\(\Rightarrow3B=\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+\frac{3}{3.4.5.6}+...+\frac{3}{26.27.28.29}\)

\(\Rightarrow3B=\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{26.27.28}-\frac{1}{27.28.29}\)

\(\Rightarrow3B=\frac{1}{1.2.3}-\frac{1}{27.28.29}\)

\(\Rightarrow3B=\frac{1}{6}-\frac{1}{21924}=\frac{3653}{21924}\)

\(\Rightarrow B=\frac{3653}{21924}:3\)

\(\Rightarrow B=\frac{3653}{65772}\)

              P/s : xong hết rùi nha !

             #~Will~be~Pens~#