# What Would This Even Look Like?

Algebra Level 5

In a sequence of real numbers $$x_{0},x_{1},x_{2},x_{3},\ldots,x_{99},x_{100}$$, for every pair of integers $$a,b$$, such that $$0 \leq a < b \leq 100$$, the sum $$x_{a}+x_{b}$$ is $$a+b$$ less than the sum of the other 99 numbers in the sequence.

As an explicit example, $$x_{0}+x_{1}=x_{2}+x_{3}+x_{4}+\cdots+x_{100}-(0+1)$$

If the value of $$x_{50}$$ can be expressed in the form $$\frac{m}{n}$$ for co-prime positive integers $$m,n$$, find the value of $$m+n$$.

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