real analysis - Proof of Uniform Convergence of continuous functions

Suppose K is compact and ${f_n}$ is a sequence of continuous functions on K which converges pointwisely to a continuous function f(x), and $f_n(x)\geq f_{n+1}(x)$ for all x $\in$ K and n $\in$ N. Show $f_n \rightarrow f$ uniformly.

My thoughts:

To prove uniform convergence I think we should use the definition(epsilon delta). But I'm not sure how to use other conditions. I was trying to combine "uniform
continuous" and "pointwise convergence" but it didn't work.

Answer

Actually, this is the Dini’s Theorem. You can see this lecture note: http://www.math.ubc.ca/~feldman/m321/dini.pdf