Show that order of $p+1$ in $\mathbb{Z}_{p^n}$ is $p^{n-1}$.

Question

I have reached till this point:

$(1 +p)^{p^{n-1}} = \sum_{k=0}^{p^{n-1}} \binom{p^{n-1}}{k} p^k$ which is further equal to $\sum_{k=0}^{n-1} \binom{p^{n-1}}{k} p^k$ in $\mathbb{Z}_{p^n}$ but don't know how to prove that $p^n$ divides every term in the latter summation other than $1$, kindly tell me how to proceed from here.