Integer part of an expression
Source: Moldova TST 2010, day 2, problem 2
March 4, 2010
trigonometryinequalities proposedinequalities
Problem Statement
Let be positive real numbers with sum . Find the integer part of:
E\equal{}x_1\plus{}\dfrac{x_2}{\sqrt{1\minus{}x_1^2}}\plus{}\dfrac{x_3}{\sqrt{1\minus{}(x_1\plus{}x_2)^2}}\plus{}\cdots\plus{}\dfrac{x_n}{\sqrt{1\minus{}(x_1\plus{}x_2\plus{}\cdots\plus{}x_{n\minus{}1})^2}}