Inegalitate in numere pozitive
Posted: Sun May 24, 2009 8:51 am
Fie \( x_1,\ x_2,\ ...,\ x_n \) numere reale strict pozitive.
Demonstrati ca: \( \frac{1}{1+x_1}+\frac{1}{1+x_1+x_2}+...+\frac{1}{1+x_1+...+x_n}<\sqrt{\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}. \)
Demonstrati ca: \( \frac{1}{1+x_1}+\frac{1}{1+x_1+x_2}+...+\frac{1}{1+x_1+...+x_n}<\sqrt{\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}. \)