(A+N)\sum_{k=0}^{p-1}(-1)^{k}N^{k}A^{-k-1}=A\sum_{k=0}^{p-1}(-1)^{k}N^{k}A^{-k-1}+N\sum_{k=0}^{p-1}(-1)^{k}N^{k}A^{-k-1}=\sum_{k=0}^{p-1}(-1)^{k}N^{k}A^{-k}+\sum_{k=0}^{p-1}(-1)^{k}N^{k+1}A^{-(k+1)}=\sum_{k=0}^{p-1}(-1)^{k}N^{k}A^{-k}+\sum_{k=1}^{p}(-1)^{k-1}N^{k}A^{-k}=(-1)^{0}N^{0}A^{0}+\sum_{k=1}^{p-1}(-1)^{k}N^{k}A^{-k}-\sum_{k=1}^{p-1}(-1)^{k}N^{k}A^{-k}-(-1)^{p}N^{p}A^{p}=I