# Live in past

Algebra Level 5

$x_{n+1}=\frac{x_n+x_n^2}{1+x_n+x_n^2}; \quad x_1=\frac{1}{2}$ If {$$x_n$$} is a sequence of numbers satisfying the recurrence relation above, find $\frac{1}{x_1+1}+\frac{1}{x_2+1}+\frac{1}{x_3+1}+......\frac{1}{x_{2012}+1}+\frac{1}{x_{2013}}$

×