1 CMR:

B=\(\frac{4}{3}+\frac{7}{3^2}+\frac{10}{3^3}+.....+\frac{3n+1}{3^n}< \frac{11}{4}\)(n thuộc N*;n>3)

A=\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}< \frac{3}{4}\)

C=\(\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+...+\frac{3^{20}-1}{3^{20}}>19\frac{1}{2}\)

Bài 1:

Chứng minh rằng:

\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)

Bài 2:

Cho \(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{70}\)

CMR: \(a)A>\frac{4}{3}\);               \(b)A< 2,5\)

Cho A= \(\frac{1}{2^2}\)+ \(\frac{1}{3^2}\)+\(\frac{1}{4^2}\)+ . . . .+ \(\frac{1}{100^2}\)

CMR : A<\(\frac{3}{4}\)

Cho \(A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{99}{100}\)

  CMR: \(\frac{1}{15}< A< \frac{1}{10}\)

cho A = \(\frac{1}{3^2}\)+\(\frac{1}{4^2}\)+...+\(\frac{1}{50^2}\)

CMR A>\(\frac{1}{4}\)va A<\(\frac{4}{9}\)

a)\(\frac{1}{10^2}+\frac{1}{11^2}+\frac{1}{12^2}+...+\frac{1}{100^2}<\frac{3}{4}\)

b)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{99}{100}\)

c)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{3}{4}\)

a) CMR: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< \frac{3}{4}\)

b) CMR: \(\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+...+\frac{1}{\left(2n+1\right)^2}< \frac{1}{4}\)