# Partial Sum of the Binomial Theorem [duplicate]

The binomial theorem states $\sum_{k=0}^nC_n^kr^k=(1+r)^n$. I am interested in the function $$\sum_{k=0}^mC_n^kr^k, \quad m<n$$ for fixed $n$ and $r$, and both $m$ and $n$ are integers. Are there any notable properties for this function? Any literature references?

In particular, do any good closed-form approximations exist for this partial sum of the binomial theorem?