\sum^{n-1}_{k=0}\hat{B}^k[\hat{A},\hat{B}]\hat{B}^{n-k-1}=\sum^{n-1}_{k=0}[\hat{A},\hat{B}]\hat{B}^{n-1}=n[\hat{A},\hat{B}]\hat{B}^{n-1}