Find a sequence {f_n} approaching uniformly on [0,1] for which the limit as 'n' approaches infinity (length of f_n on [0,1]) is not equal to length of 'f' on [0,1]

Question

anonymous · Answer

Sorry, "...approaching 'f' uniformly..."* (if that wasn't obvious)

anonymous · Answer

First I would just try a few uniformly convergent sequences and see if you'll got lucky, but I can't even come up with such a nontrivial sequence.

Also does such a sequence even exist, because you get all sorts of nice properties from uniform convergence.

anonymous · Answer

nvm, got it

anonymous · Answer

So what sequence did you use?

anonymous · Answer

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Length of each f_n is 2 since the length of 2 sides of an equilateral triangle are twice the other side