# 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.