Chứng minh:

\(\frac{1}{3}\). \(\frac{4}{6}\). \(\frac{7}{9}\).....\(\frac{208}{210}\)< \(\frac{1}{25}\). 

Cho A=\(\frac{1}{3}x\frac{4}{6}x\frac{7}{9}x.....x\frac{208}{210}\)

  Chứng minh :A<\(\frac{1}{25}\)

  Cho A=\(\frac{1}{3}.\frac{4}{6}\frac{7}{9}.\frac{10}{12}...\frac{208}{210}\)

   CMR: \(\frac{1}{52}

Cho A=1-\(\frac{1}{2}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)+...+\(\frac{7}{12}\)-\(\frac{1}{50}\)

Chứng minh rằng 7/12<A<5/6

  Chứng minh rằng:

\(a,\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+........\frac{1}{9}< 2\)

\(b,\frac{1}{6}+\frac{1}{7}+......+\frac{1}{19}< 2\)

\(c,\frac{1}{10}+\frac{1}{11}+......+\frac{1}{28}>1\)

Bài 1 : Cho A = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}...\frac{79}{80}\)

Chứng minh rằng A < \(\frac{1}{9}\)

Bài 4 : Chứng minh rằng:  1.3.5.7....19 = \(\frac{11}{2}.\frac{12}{2}.\frac{13}{2}...\frac{20}{2}\)

Chứng minh rằng:

a) \(\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+...+\frac{1}{100!}<1\)

b) \(\frac{9}{10!}+\frac{9}{11!}+\frac{9}{12!}+...+\frac{9}{1000!}<\frac{1}{9!}\)

Chứng minh rằng:

a) \(\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+...+\frac{1}{100!}<1\)

b) \(\frac{9}{10!}+\frac{9}{11!}+\frac{9}{12!}+...+\frac{9}{1000!}<\frac{1}{9!}\)