# Uniform Convergence of nx/nx+1

1. Oct 24, 2011

### hmmmmm

I am given $$f_n(x)=\frac{nx}{nx+1}$$ defined on $$[0,\infty)$$ and I have that the function converges pointwise to $$0 \ \mbox{if x=0 and} 1\ \mbox{otherwise}$$

Is the function uniform convergent on $$[0,1]$$?

No. If we take x=1/n then $$Limit_{n\rightarrow\infty}|\frac{1/n*n}{1+1/n*n}-1|=0.5$$

which implies that $$Limit_{n\rightarrow\infty} sup |f_n(x)-1|$$ is not 0.

I am then asked if it converges uniformly on the interval $$(0,1]$$ which I think it does but how do I show that $$Limit_{n\rightarrow\infty} sup |f_n(x)-1|$$=0?

thanks for any help

Last edited by a moderator: Oct 26, 2011
2. Oct 24, 2011

### mathman

Your latex is screwed up.

3. Oct 26, 2011

### hmmmmm

Yeah do you know why that is?

thanks for any help

4. Oct 26, 2011

### willem2

don't put TEX in capitals.