## Interesting problem from my analysis class

Let n be a positive integer and suppose $$f$$ is continuous on $$[0,1]$$ and $$f(0) = f(1)$$. Prove that the graph of $$f$$ has a horizontal chord of length $$1/n$$. In other words, prove there exists $$x \in [0,(n - 1)/n]$$ such that $$f(x+1/n) = f(x)$$

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 no one even wants to try?
 hint: write f(1) - f(0) as a telescoping sum.

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## Interesting problem from my analysis class

 Quote by StonedPanda no one even wants to try?
I would hazard a guess that people are suspicious that this is your homework.

 Recognitions: Homework Help Is f differentiable, or just continuous?
 Recognitions: Homework Help Science Advisor seems trivial. indeed trivial for all numbers less than or equal to 1, not just 1/n. after thinking about an actual proof for a few minutes let me rephrase that as "intuitively plausible", rather than "trivial". it apparently follows from the intermediate value theorem but the details seem tedious, even elusive. cute problem.
 Recognitions: Homework Help Science Advisor assume f(x) non negative, then what?