Các câu hỏi tương tự
\(\frac{1}{5^1}+\frac{1}{5^2}+\frac{1}{5^3}+......+\frac{1}{5^{2008}}<\frac{1}{4}\) Chứng minh hộ mình với
\(S=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)
S=?
Giá trị của biểu thức \(A=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)là \(A=.............\)
chứng minh\(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2012}-\frac{1}{2013}+\frac{1}{2014}< \frac{2}{5}\)
chứng minh \(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{2012}-\frac{1}{2013}+\frac{1}{2014}< \frac{2}{5}\)
Giúp mình bài này với
Tính
\(A=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+.....+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+.....+\frac{1}{2008}+\frac{1}{2009}}\)
Chứng minh rằng:
a,\(\frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+...+\frac{5}{\left(4n-1\right).\left(4n+3\right)}=\frac{5n}{3.\left(4n+3\right)}\)
b,\(\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+100}< \frac{1}{4}\)
chứng minh A=B biết :A=\(\frac{\left(3\frac{1}{15}+\frac{1}{5}\right):2\frac{1}{2}}{\left(5\frac{3}{7}-2\frac{1}{4}\right):4\frac{43}{56}}\) ; B= \(\frac{1,2:\left(1\frac{1}{5}.1\frac{1}{4}\right)}{0,32+\frac{2}{5}}\)
Chứng minh rằng
a) \(\frac{1}{5}<\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{98}-\frac{1}{99}<\frac{2}{5}\)
b) \(\frac{1}{15}<\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}<\frac{1}{10}\)