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=\(\frac{3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{49\cdot51}{50\cdot50}\)
=\(\frac{\left(2\cdot3\cdot...\cdot49\right)\cdot\left(3\cdot4\cdot...\cdot51\right)}{\left(2\cdot3\cdot4\cdot...\cdot50\right)\left(2\cdot3\cdot4\cdot...\cdot50\right)}\)
=\(\frac{51}{50\cdot2}=\frac{51}{100}\)
A = \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.......\frac{2499}{2500}\)
A = \(\frac{1.3.2.4.3.5.......49.51}{2.2.3.3.4.4........50.50}\)
A = \(\frac{\left(1.2.3.......49\right).\left(3.4.5.....51\right)}{\left(2.3.4.....50\right)\left(2.3.4.....50\right)}\)
A = \(\frac{51}{50.2}\)
A = \(\frac{51}{100}\)
A = \(\frac{1.3}{2.2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\cdot\cdot\cdot\cdot\frac{49\cdot51}{50\cdot50}=\frac{1\cdot3\cdot2\cdot4\cdot...\cdot49\cdot51}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot\cdot\cdot\cdot50\cdot51}=\frac{1\cdot51}{2\cdot50}=\frac{51}{100}\)
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
\(A=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}...\frac{49.51}{50^2}\)
\(A=\frac{1.2.3...49}{2.3.4...50}.\frac{3.4.5...51}{2.3.4...50}\)
\(A=\frac{1}{50}.\frac{51}{2}\)
\(A=\frac{51}{100}\)
\(A=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}.....\dfrac{899}{30^2}\)
\(A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{29.31}{30.30}\)
\(A=\dfrac{1.3.2.4.3.5.....29.31}{2.2.3.3.4.4.....30.30}\)
\(A=\dfrac{1.2.3.....29}{2.3.4....30}.\dfrac{3.4.5.....31}{2.3.4.....30}\)
\(A=\dfrac{1}{30}.\dfrac{31}{2}=\dfrac{31}{60}\)
\(B=\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{2499}{2500}\)
\(B=\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.\dfrac{4.6}{5.5}.....\dfrac{49.51}{50.50}\)
\(B=\dfrac{2.4.3.5.4.6.....49.51}{3.3.4.4.5.5....50.50}\)
\(B=\dfrac{2.3.4......49}{3.4.5....50}.\dfrac{4.5.6.....51}{3.4.5....50}\)
\(B=\dfrac{2}{50}.\dfrac{51}{3}=\dfrac{17}{25}\)
Giải:
\(A=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}.....\dfrac{899}{30^2}.\)
\(A=\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}.....\dfrac{29.31}{30^2}.\)
\(A=\dfrac{1.2.3.....29}{2.3.4.....30}.\dfrac{2.3.4.....31}{2.3.4.....30}.\)
\(A=\dfrac{1}{30}.31=\dfrac{30}{31}.\)
Vậy \(A=\dfrac{30}{31}.\)
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!
Trả lời:
\(A=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{2499}{2500}\)
\(=\frac{3\cdot8\cdot15\cdot...\cdot2499}{4\cdot9\cdot16\cdot...\cdot2500}\)
\(=\frac{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot49\cdot51}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot50\cdot50}\)
\(=\frac{\left(1\cdot2\cdot3\cdot...\cdot49\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot51\right)}{\left(2\cdot3\cdot4\cdot...\cdot50\right)\left(2\cdot3\cdot4\cdot...50\right)}\)
\(=\frac{1\cdot51}{50.2}=\frac{51}{100}\)