# 10 sec challenge 7

Algebra Level 4

$\large \dfrac{x^{100}}{1+x+x^{2}+x^{3}+ \cdots +x^{200}}$

For $$x>0$$, the maximum value of the expression above is $$\dfrac{1}{N}$$ for some integer $$N$$. Find $$N$$.

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