a=8/9+15/16+24/25+....+2499/2500

a=(1-1/9)+(1-1/16)+(1-1/25)+....+(1-1/2500)

a=1-1/9+1-1/16+1-1/25+....+1-1/2500

a=(1+1+...+1)-(1/9+1/16+1/25+....+1/2500)

\(\Leftrightarrow A=\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4.4}...\frac{49.51}{50.50}\)

\(\Rightarrow A=\frac{2\cdot4\cdot3\cdot5\cdot...\cdot49.51}{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot50\cdot50}\)

\(\Rightarrow A=\frac{2\cdot51}{3\cdot50}\)

\(\Rightarrow A=\frac{17}{25}\)

17/25

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=2.4/3^2.3.5/4^2.4.6/5^2.....49.51/50^2

=(2.3.4.....49).(4.5.6.....51)/(3.4.5.....50).(3.4.5.....50)

=2.51/50.3

=17/25

giỏi hậy

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

\(=\frac{1}{3}-\frac{1}{21}\)

\(=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}\)

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

\(A=\frac{1}{3}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)+...+\left(\frac{1}{19}-\frac{1}{19}\right)-\frac{1}{21}\)

\(A=\frac{1}{3}-\frac{1}{21}\)

\(A=\frac{2}{7}\)

\(B=\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}+...+\frac{3}{68.71}\)

\(=\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}+...+\frac{1}{68}-\frac{1}{71}\)

\(=\frac{1}{11}-\frac{1}{71}\)

\(=\frac{71}{781}-\frac{11}{781}\)

\(=\frac{60}{781}\)

\(\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\cdot\frac{2499}{2500}\)

=\(\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot\cdot\cdot\cdot\cdot\frac{49\cdot51}{50\cdot50}\)

=rút gọi tử và mẫu

=\(\frac{2}{3}\cdot\frac{50}{51}\)

=\(\frac{100}{153}\)

A = 89 .1516 .2425 ....24992500 

 \(A=\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}.....\frac{49.51}{50.50}\)

\(A=\frac{2.3.4.....49}{3.4.5.....50}.\frac{4.5.6.....51}{3.4.5....50}\)

\(A=\frac{2}{50}.\frac{51}{3}\)

\(A=\frac{17}{25}\)

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