8/9 x 15/16 x 24/25 x...x 2499/2500

=   \(\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}\times\frac{4\times6}{5\times5}\times...\times\frac{49\times51}{50\times50}\)

=   \(\frac{2\times4\times3\times5\times4\times6\times...\times49\times51}{3\times3\times4\times4\times5\times5\times...\times50\times50}\)

= \(\frac{2\times51}{3\times50}\)

= \(\frac{17}{25}\)

\(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}....\frac{2499}{2500}=\frac{8.15...2499}{9.16...2500}=\frac{2.4.3.5...49.51}{3.3.4.4...50.50}=\frac{\left(2.3.4...49.50\right).\left(4.5...49.51\right)}{\left(2.3.4...49.50\right).\left(3.4.5...49.50\right)}=\frac{51}{3.50}\)\(=\frac{17}{50}\)

a:Sửa đề: 1x3+2x4+...+99x101

\(=1\times\left(1+2\right)+2\times\left(2+2\right)+\cdots+99\times\left(99+2\right)\)

\(=\left(1\times1+2\times2+\cdots+99\times99\right)+2\times\left(1+2+\cdots+99\right)\)

\(=\frac{99\times\left(99+1\right)\times\left(2\times99+1\right)}{6}+2\times\frac{99\times100}{2}\)

\(=\frac{99\times100\times199}{6}+99\times100=33\times50\times199+99\times100\)

\(=33\times50\times\left(199+3\times2\right)=33\times50\times205=338250\)

b: \(\frac89\times\frac{15}{16}\times\ldots\times\frac{2499}{2500}\)

\(=\left(1-\frac19\right)\times\left(1-\frac{1}{16}\right)\times\ldots\times\left(1-\frac{1}{2500}\right)\)

\(=\left(1-\frac13\right)\times\left(1-\frac14\right)\times\ldots\times\left(1-\frac{1}{50}\right)\times\left(1+\frac13\right)\times\left(1+\frac14\right)\times\ldots\times\left(1+\frac{1}{50}\right)\)

\(=\frac23\times\frac34\times\ldots\times\frac{49}{50}\times\frac43\times\frac54\times\ldots\times\frac{51}{50}=\frac{2}{50}\times\frac{51}{3}=\frac{17}{25}\)

= 2x4/3x3 x 3x5/4x4 x 4x6/5x5 x.....x 49x51/50x50

= 2x4x3x5x4x6x...49x51/ 3x3x4x4x5x5...50x50

= 2x51/3x50

= 17/25 

\(\frac{8}{9}\). \(\frac{15}{16}\). \(\frac{24}{25}\). ..... . \(\frac{2499}{2500}\)

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

= \(\frac{2.4.3.5.4.6.49.51}{3.3.4.4.5.5.....50.50}\)= \(\frac{2.51}{3.50}\)= \(\frac{17}{25}\)

17/25 nha bạn

Đề bài yêu cầu làm j z bn

\(=\frac{2.4}{3^2}.\frac{3.5}{4^2}....\frac{49.51}{50^2}\)

\(=\frac{2.3....49}{3.4....50}.\frac{4.5....51}{3.4....50}\)

\(=\frac{2}{50}.\frac{17}{1}\)

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

Ta có : \(A=\frac{8}{9}.\frac{15}{16}.....\frac{2499}{2500}\)

\(A=\frac{8.15.....2499}{9.16.....2500}\)

\(A=\frac{\left(2.4\right).\left(3.5\right).....\left(49.51\right)}{\left(3.3\right).\left(4.4\right).....\left(50.50\right)}\)

\(A=\frac{\left(2.3....49\right).\left(4.5....51\right)}{\left(3.4....50\right).\left(3.4.....50\right)}\)

\(A=\frac{2\left(3.4.....49\right).\left(4.5.....50\right).51}{\left(3.4.....49\right).50.3.\left(4.5.....50\right)}\)

\(A=\frac{2.51}{3.50}\)

\(A=\frac{2.17.3}{3.25.2}\)

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