Neumann series

If $A$ is a square matrix, , then $I-A$ is nonsingular and${(I-A)}^{-1}=I+A+A^2+\mathrm{\cdots }={\sum }_{k=0}^{\mathrm{\infty }}{A}^k$. This is the Neumann series.
It provides approximations of ${(I-A)}^{-1}$when $A$ has entries of small magnitude.For example, a first-order approximation is ${(I-A)}^{-1}\approx I+A$.
It is obvious that this is a generalization of the geometric series.