Cho \(S=\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+...+\frac{2^{n+1}}{2005^{^{2^n}}+1}+...+\frac{2^{2006}}{2006^{2^{2005}}+1}\). So sánh S với \(\frac{1}{1002}\)

Cho \(S=\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+\frac{2^3}{2005^{2^2}+1}+...+\frac{2^{n+1}}{2005^{2^{n+1}}+1}+...+\frac{2^{2006}}{2005^{2^{2006}}+1}\)

So sánh S với \(\frac{1}{1002}\)

Cho S=\(\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+\frac{2^3}{2005^{2^2}}+...\)\(..+\frac{2^{n+1}}{2005^{2^n}}+...+\frac{2^{2006}}{2005^{2^{2005}}+1}\)

So sánh S với \(\frac{1}{1002}\)

\(S=\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+\frac{2^3}{2005^{2^2}+1}+...+\frac{2^{n+1}}{2005^{2^n}+1}+...+\frac{2^{2006}}{2005^{2^{2005}}+1}\)So sánh S với \(\frac{1}{1002}\)

Tính: S

S= \(\frac{2}{2005+1}\) + \(\frac{2^2}{2005^2+1}\)+ \(\frac{2^3}{2005^{2^2}+1}\)+ \(\frac{2^4}{2005^{2^3}+1}\)+ .... + \(\frac{2005^{2006}}{2005^{2^{2005}}+1}\)+ .... + \(\frac{2^{n+1}}{2005^{2^n}+1}\)

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 S= \(\frac{2}{2005+1}+\frac{2}{2005^2+1}+\frac{2}{2005^{2^2}+1}+....+\frac{2}{2005^{2^{2005}}}\). SO SÁNH S VỚI \(\frac{1}{1002}\)

So sánh:

a) S= \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+.....+\frac{2}{2010.2011.2012}với\frac{1}{2}\)

b) A=\(\frac{10^{2004}+1}{10^{2005}+1}vàB=\frac{10^{2005}+1}{10^{2006}+1}\)

Tinh A = \(\frac{\frac{2006}{1}+\frac{2006}{2}+\frac{2006}{3}+........\frac{2006}{2006}+\frac{2006}{2007}}{\frac{1}{2006}+\frac{2}{2005}+\frac{3}{2004}+.........+\frac{2005}{2}+\frac{2006}{1}}\)