Originally Posted by

**roninpro** Are you trying to use the Weierstrass M-Test? It isn't applicable here since we are not looking at a function defined by an infinite series.

You need to use the definition of uniform convergence: Given any $\displaystyle \varepsilon>0$, there is $\displaystyle N$ so that whenever $\displaystyle n>N$, $\displaystyle |f_n(x)-f(x)|<\varepsilon$ for all $\displaystyle x\in [0,1]$. (Now I realise that you are restricted to $\displaystyle [0,1]$ - sorry for the confusion earlier.) Can you find such an $\displaystyle N$? You should take the point $\displaystyle x=1$ into consideration.