Chứng minh rằng:

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

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

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

Chứng minh rằng :\(\frac{1}{10}\)+ \(\frac{1}{11}\)+......+\(\frac{1}{19}\)< 1

Bài 1:So sánh(bằng 2 cách):

\(A=\frac{10^{11}-1}{10^{12}-1}\)\(B=\frac{10^{10}+1}{10^{11}+1}\)

Bài 2:Chứng minh:

\(\frac{3}{5}< \frac{1}{31}+\frac{1}{32}+\frac{1}{33}+..........+\frac{1}{59}+\frac{1}{60}< \frac{4}{5}\)

Cho:

\(A=\frac{1}{10}+\frac{1}{11}+...+\frac{1}{39}\)

Chứng minh rằng: \(A< \frac{11}{6}\)

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

1,a,Tính tổng M:\(\frac{10}{56}\)+\(\frac{10}{140}\)+\(\frac{10}{260}\)+...+\(\frac{10}{1400}\)

b,Cho S=\(\frac{3}{10}\)+\(\frac{3}{11}\)+\(\frac{3}{12}\)+\(\frac{3}{13}+\frac{3}{14}\).Chứng minh 1<s<2