# Math Help - Sequence of function 2

1. ## Sequence of function 2

Let $(f_n)^\infty_{n=1}$ a sequence of function which defined recursively on interval $[a,b]$:

$f_n(x)=\sqrt{xf_{n-1}(x)}$, $f_0(x)\equiv1$

1. Prove that the sequence $(f_n)^\infty_{n=1}$ converges on interval $[a,b]$ to limit continuous function $f$.

2. Prove that the convergence is uniform.

2. See the attachment.