Enjoy the sequence!

\[\large \sqrt{a_{2}+a_{3}+\cdots+a_{99}}-\sqrt{a_{1}+a_{100}} \]

Let \(a_{1},a_{2},a_{3},\ldots,a_{100}\) is an sequence of consecutive positive integers.

Find the minimum integer value of the expression above. of \ which is an integer.


From Thai High School Maths Exam 2013
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