Calculate the Logarithm of a square matrix

Using Taylor series we can approximate an analitic function to a polinomial, for example, is well known that

and

Also, matrix multiplication allows us to define the exponential matrix, which is the matrix

and the natural logarithm of a matrix, which is the matrix

Where A is a square matrix. Since has been proved that these series indeed exist (converges), one might want to know how the matrix or the natural log of A looks like for a given . This code allows to compute such matrices for a given number of user-specified addends.