Các câu hỏi tương tự
\(S=\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+\frac{2^3}{2005^{2^2}+1}+...+\frac{2^{n+1}}{2005^{2^n}+1}+...+\frac{2^{2006}}{2005^{2^{2005}}+1}\)So sánh S với \(\frac{1}{1002}\)
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 \(\frac{1}{1002}\)
Cho S= \(\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+\frac{2^3}{2005^{2^2}+1}+........+\frac{2^{n+1}}{2005^{2^n}+1}+.......+\frac{2^{2006}}{2005^{2^{2006}}+1}\)
So sánh S với \(\frac{1}{1002}\)
Cho \(S=\frac{2}{2005+1}+\frac{2^2}{2005^2+1}+\frac{2^3}{2005^{2^2}+1}+...+\frac{2^{n+1}}{2005^{2^{n+1}}+1}+...+\frac{2^{2006}}{2005^{2^{2006}}+1}\)
So sánh S với \(\frac{1}{1002}\)
Tinh A = \(\frac{\frac{2006}{1}+\frac{2006}{2}+\frac{2006}{3}+........\frac{2006}{2006}+\frac{2006}{2007}}{\frac{1}{2006}+\frac{2}{2005}+\frac{3}{2004}+.........+\frac{2005}{2}+\frac{2006}{1}}\)
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 \(\frac{1}{1002}\)
Chứng minh :\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+......+\frac{1}{2005^2}< \frac{3}{4}\)
Bài 1 :
1 . Tính :
\(P=\frac{\frac{1}{2003}+\frac{1}{2004}-\frac{1}{2005}}{\frac{5}{2003}+\frac{5}{2004}-\frac{5}{2005}}-\frac{\frac{2}{2002}+\frac{2}{2003}-\frac{2}{2004}}{\frac{3}{2002}+\frac{3}{2003}-\frac{3}{2004}}\)
2 . Biết : 13 + 23 + ... + 103 = 3025
Tính : S = 23 + 43 + 63 + .... + 203
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 \(\frac{1}{1002}\)
\(S=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)
S=?