# Tetration And Telescoping

Calculus Level 5

$\large \sum_{x=2}^\infty \sum_{n=0}^\infty \dfrac{2^n}{1 + x^{2^n}} (-1)^x$

The iterated series above has a closed form.

Let this closed form be denoted by $$\omega$$, submit your answer as $$\lfloor 1000 \omega \rfloor$$.

 Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

×