How can I prove that $f_n(x)=2/\sqrt n$ is uniformly convergent to cero in the interval $x \in (0, \infty)$? It obviously the sequence goes to cero but I would like to bound the limit with another function in order to use the definition of uniform convergence.
For any $\epsilon >0, \exists n_0\in N:$ any $n> n_o, |f_n-f|<\epsilon$
Thank you very much!!
You want $n$ such that $|\frac{2}{\sqrt{n}}|<\epsilon$. Rearrange to obtain an expression (inequality) for $n$ in terms of $\epsilon$.