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x1001+x+x2+x3+⋯+x200 \large \dfrac{x^{100}}{1+x+x^{2}+x^{3}+ \cdots +x^{200}} 1+x+x2+x3+⋯+x200x100
For x>0x>0x>0, the maximum value of the expression above is 1N\dfrac{1}{N}N1 for some integer NNN. Find NNN.
This is a part of 10-seconds challenge.
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