(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We know that f is uniformly continuous.

For each n in N, we define f_{n}(x)=f(x+1/n) (for all x in R).

Show that f_{n}converges uniformly to f.

2. Relevant equations

http://en.wikipedia.org/wiki/Uniform_convergence

3. The attempt at a solution

I know that as n approaches infinity, that f_{n}(x)=f(x), which implies that f_{n}converges to f.

I'm currently trying to apply the fact that if f_{n}is uniformly convergent, then

lim_{n->infinity}Sup {f_{n}(x): x in R}=0.

But I keep getting stuck on the fact that there's an function in the definition of f_{n}i.e., f_{n}(x)=f(x+1/n). Is there a way to work with it?

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# Homework Help: Uniform convergence of a series

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