Arranging numbers in a circle
Here's a question I found from a Chinese book, (which contains no answers), and I found it to be very interesting.
Suppose we have numbers whose sum is 0.
Arrange them in a fixed order in a circular manner.
Show that there exists an integer m, such that , and the sum of any number (1 to n) of consecutive terms starting with is non-negative. (Clockwise direction)
It seems that it is true, after trying with a few numbers.
How do you actually prove it?
Thanks in advance.