\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.......\frac{899}{900}=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{29.31}{30.30}=\frac{1.2.3.....29}{2.3.4......30}.\frac{3.4.5......31}{2.3.4......30}\)
\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
chứng tỏ rằng 1/5 + 1/6 + 1/7 + .....+ 1/17 < 2
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{99}{100}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{9.11}{10.10}\)
\(=\frac{\left(1.2.3...9\right).\left(3.4.5...11\right)}{\left(2.3.4...10\right).\left(2.3.4...10\right)}\)
\(=\frac{1}{10}.\frac{11}{2}=\frac{11}{20}\)
A=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}..........\frac{899}{900}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{29.31}{30.30}\)
\(=\frac{1.3.2.4.3.5...........29.31}{2.2.3.3.4.4.......30.30}\)
\(=\frac{\left(1.2.3........29\right).\left(3.4.5..........31\right)}{\left(2.3.4..........30\right).\left(2.3.4........30\right)}\)
\(=\frac{1.31}{2.30}\)
\(=\frac{31}{60}\)