#)Giải :
\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{2499}{2500}\)
\(A=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times\frac{4.6}{5.5}\times...\times\frac{49.51}{50.50}\)
\(A=\frac{1\times3\times2\times4\times3\times5\times...\times49\times51}{2\times2\times3\times3\times4\times4\times...\times50\times50}\)
\(A=\frac{1\times51}{2\times50}\)
\(A=\frac{51}{100}\)
\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{2499}{2500}\)
\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times\frac{6\times4}{5\times5}\times...\times\frac{49.51}{50\times50}\)
\(=\frac{1}{2}\times\frac{51}{50}\)
\(=\frac{51}{100}\)
\(a=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x\frac{24}{25}x......x\frac{2499}{2500}\)
\(a=\frac{1x3}{2x2}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x\frac{6x4}{5x5}x.....x\frac{49x51}{50x50}\)( Phần này thì tối giản nha ! )
\(a=\frac{1}{2}x\frac{51}{50}\)
\(a=\frac{51}{100}\)
~ Hok tốt ~
