Chứng minh rằng :

a)\(\frac{1}{2}\)-\(\frac{1}{4}\)+\(\frac{1}{8}\)-\(\frac{1}{16}\)+\(\frac{1}{32}\)-\(\frac{1}{64}\)<\(\frac{1}{3}\)

b)\(\frac{1}{3}\)-\(\frac{2}{3^2}\)+\(\frac{3}{3^3}\)-\(\frac{4}{3^4}\)+......+\(\frac{99}{3^{99}}\)-\(\frac{100}{3^{100}}\)<\(\frac{3}{16}\)

a) \(Cho\)\(S=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+.....+\frac{1}{60}\)

\(Chứng\) \(minh\) \(\frac{3}{5}< S< \frac{4}{5}\)

b) \(Chứng\)\(minh\)\(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+.....+\frac{1}{100}>\frac{7}{10}\)

c) \(Chứng\)\(minh\)\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\) không là số tự nhiên

d) \(Chứng\)\(minh\)\(\frac{1}{5}< D< \frac{1}{10}\) \(với\)\(D=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{99}{100}\)

chứng minh :

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

b,B=1+\(\frac{1}{2}\)+\(\frac{1}{3}\)+\(\frac{1}{4}\)+...+\(\frac{1}{63}\)< 6

c,C=\(\frac{1}{2}\).\(\frac{3}{4}\).\(\frac{5}{6}\).\(\frac{7}{8}\)...\(\frac{9999}{10000}\)< \(\frac{1}{100}\)

Bai 1: Cho \(A\) = \(\left(\frac{1}{2^2}-1\right)\)\(.\)\(\left(\frac{1}{3^2}-1\right)\)\(.\)\(\left(\frac{1}{4^2}-1\right)\)\(...\)\(\left(\frac{1}{100^2}-1\right)\)\(.\)So sánh  \(A\)với \(\frac{-1}{2}\)

Bai 2;Chứng minh rằng;

           a) \(\frac{3}{1^2.2^2}\)+   \(\frac{5}{2^2.3^2}\)+   \(\frac{7}{3^2.4^2}\)+ ... +   \(\frac{19}{9^2.10^2}\)\(< \)\(1\)

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