Abstract
Some additive results for the Drazin inverses are investigated under conditions weaker than those used in some recent papers on this subject. In particular, a formula is given for the Drazin inverse of a sum of two matrices $$P, Q\in {\mathbf {C}}^{n\times n}$$ with $$PQ^{i}P=0$$ for positive integer $$i=1,2,\ldots ,n$$ . As an application we give some new representations for the Drazin inverse of a $$2 \times 2$$ block matrix.
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