Chứng minh rằng:

\(3<\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+...+\frac{5}{49}<8\)

chứng minh rằng \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}.......\frac{9999}{1000}< \frac{1}{100}\)

Chứng minh rằng

\(\frac{5}{1.2.3}+\frac{8}{2.3.4}+\frac{11}{3.4.5}+...+\frac{6038}{2012.2013.2014}<2\)

Chứng minh rằng \(\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times\frac{7}{8}\times...\times\frac{99}{100}< 0,01\)

chứng minh rằng A =\(\frac{1}{4}.\frac{3}{6}.\frac{5}{8}.....\frac{43}{46}.\frac{45}{48}\)<\(\frac{1}{133}\)

\(ChoA=\frac{1}{100}+\frac{1}{101}+...+\frac{1}{199}\)

Chứng minh rằng: \(A>\frac{5}{8}\)

Cho A = \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)

\(a,\) Chứng minh rằng \(A>\frac{7}{12}\)

b) Chứng minh : \(A>\frac{5}{8}\)

Cho G=\(\frac{5}{3}+\frac{8}{3^2}+\frac{11}{3^3}+...+\frac{302}{3^{100}}\)

Chứng minh rằng 11/3<G<7/2

Cho:

\(A=\frac{1+5+5^2+...+5^9}{1+5+5^2+...+5^8};B=\frac{1+3+3^2+...+3^9}{1+3+3^2+...+3^8}\)

Chứng minh rằng A>B