cmr:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2005^3}+\frac{1}{2006^3}<\frac{1}{4}\)
giúp mk vs nhak
Chứng minh rằng: \(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}...+\frac{1}{2005^3}+\frac{1}{2006^3}>\frac{1}{15}\)
Chứng minh: A=\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2005^3}+\frac{1}{2006^3}<\frac{1}{4}\)
C=\(\frac{\frac{2006}{2}}{\frac{2006}{1}}\) +\(\frac{2006}{\frac{3}{\frac{2005}{2}}}\) +\(\frac{2006}{\frac{4}{\frac{2004}{3}}}\) +...+\(\frac{2006}{\frac{2007}{\frac{1}{2006}}}\)
Chứng minh rằng :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}=\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}_{ }\)
Cho \(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{2005}}\)
CMR:\(B< \frac{1}{2}\)
Tính:
S = \(\frac{2}{2005+1}\)+ \(\frac{2^2}{2005^2+1}\)+ \(\frac{2^3}{2005^{2^2}+1}\)+ \(\frac{2^4}{2005^{2^3}+1}\)+ ...+ \(\frac{2^{n+1}}{2005^{2^n}+1}\)+ ...+ \(\frac{2^{2006}}{2005^{2^{2005}}+1}\)
Cho B=\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+......+\frac{1}{3^{2005}}\)
CMR B < \(\frac{1}{2}\)
Tính: S
S= \(\frac{2}{2005+1}\) + \(\frac{2^2}{2005^2+1}\)+ \(\frac{2^3}{2005^{2^2}+1}\)+ \(\frac{2^4}{2005^{2^3}+1}\)+ .... + \(\frac{2005^{2006}}{2005^{2^{2005}}+1}\)+ .... + \(\frac{2^{n+1}}{2005^{2^n}+1}\)
