# Find Sequence, get the series

Algebra Level 4

The sequence $$\left\{ { x }_{ n } \right\}$$ is defined by $$x_1 = \dfrac{1}{2}$$ and $$x_{k+1} = x_k + x_k^2$$ for $$k \ge 2$$. Then find

$\left\lfloor \frac { 1 }{ { x }_{ 1 }+1 } +\frac { 1 }{ { x }_{ 2 }+1 } +\cdots +\frac { 1 }{ { x }_{ 100 }+1 } \right\rfloor$

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