Cho \(B=\frac{1}{1.1.3}+\frac{1}{2.3.5}+\frac{1}{3.5.7}+...+\frac{1}{100.199.201}\)
So sánh \(B\) và \(\frac{2}{3}\)
Tính
\(\frac{20}{2.3.5}+\frac{20}{3.5.7}+\frac{20}{5.7.9}+...+\frac{20}{25.27.29}\)
3 k 1 lượt lm
Cho A = \(\frac{1}{1.3.5}\) + \(\frac{1}{3.5.7}\) + ..... + \(\frac{1}{47.49.51}\). Chứng minh A < \(\frac{1}{12}\)
So sánh ;
\(A=\frac{1}{101^2}+\frac{1}{102^2}+....+\frac{1}{105^2};\frac{1}{2^2.3.5^2.7}\)
So sánh A và B biết:
\(A=\frac{1}{101^2}+\frac{1}{102^2}+\frac{1}{103^2}+\frac{1}{104^2}+\frac{1}{105^2}\)và \(B=\frac{1}{2^2.3.5^2.7}\)
So sánh
\(\frac{2^{2006}+7}{2^{2004}+7}\)và \(\frac{2^{2003}+1}{2^{2001}+1}\)
\(\frac{1}{101^2}+\frac{1}{102^2}+\frac{1}{103^2}+\frac{1}{104^2}+\frac{1}{105^2}\)và \(\frac{1}{2^2.3.5^2.7}\)
Chứng minh rằng : \(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
Chứng minh rằng : \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)
1.chứng minh rằng : \(\frac{1}{2}!+\frac{2}{3}!+\frac{3}{4}!+...+\frac{99}{100}!< 1\)
2. Chứng minh rằng :\(\frac{1.2-1}{2}+\frac{2.3-1}{3}+\frac{3.4-1}{4}+...+\frac{99.100-1}{100}< 2\)
So sánh A và B biết
\(A=\) \(\frac{1}{101^2}+\frac{1}{102^2}+\frac{1}{103^2}+\frac{1}{104^2}+\frac{1}{105^2}\)và \(B=\frac{1}{2^2.3.5^2.7}\)