# 1 2 3 Go

Algebra Level 5

$$\sqrt{\left( \displaystyle \sum_{i=1}^{100} (101-i)x_{i}\right) + 1 } + \sqrt{\left( \displaystyle \sum_{j=1}^{100} jx_{j} \right) + 2 } + \sqrt{\left( \displaystyle \sum_{k=1}^{100} 101x_{k}\right ) + 3 }$$

If $$x_{1}, x_{2}, \ldots, x_{100}$$ are 100 positive reals such that $$x_{1} + x_{2} + x_{3} + \cdots + x_{100} = 1$$, find the maximum value of the expression above.

Let it be of the form $$a\sqrt{b}$$, where $$b$$ is square free and $$a,b \in \mathbb{N}$$. Enter $$(a+b)$$ as your answer.

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