# I am boxing sequences

Algebra Level 5

Let $$\{ x _n \}$$ be a sequence defined such that $${ x }_{ k+1 }={ { x_{ k } }^{ 2 } } +{ x }_{ k }$$ with $$x_1 = \frac 1 2$$.

Find the greatest integer less than or equals to the expression below.

$\large \frac { 1 }{ { x }_{ 1 }+1 } +\frac { 1 }{ { x }_{ 2 }+1 } + \ldots + \frac { 1 }{ { x }_{ 100 }+1 }$

×