10-seconds challenge-7

Algebra Level 4

x1001+x+x2+x3++x200 \large \dfrac{x^{100}}{1+x+x^{2}+x^{3}+ \cdots +x^{200}}

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


This is a part of 10-seconds challenge.

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