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)

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

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

=rút gọi tử và mẫu

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

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

A = 89 .1516 .2425 ....24992500 

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

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

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

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

Study well 

Bạn vào https://sites.google.com/site/toantieuhocpl/20-tinh-nhanh sẽ có đấy.

=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=8/9.15/16.24/25.....2499/2500

A=2.4/3^2 . 3.5/4^2 . 4.6/5^2 ..... 49.51/50^2

A=2.3.4......49/3.4.5.....50 . 4.5.6......51/3.4.5.....50

A=1/25 (rút gọn từ 2/50) . 51/3

A=51/75

tích nha!

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

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

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

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

17/25

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