The complex function z = 0 is the m-order pole of function 1 / Z ^ 2 + 1 / Z ^ 3, M =?

The complex function z = 0 is the m-order pole of function 1 / Z ^ 2 + 1 / Z ^ 3, M =?

LIM (Z tends to 0) (1 / Z ^ 2 + 1 / Z ^ 3) Z ^ 3 = 1, which is a constant,
So it's the third-order pole, M = 3

What kind of singularities does (LN (Z + 1)) / Z function have? If it is a pole, point out its order?

Since f (z) = ln (1 + Z) / Z is not analytic, only z = 0, and the series expansion of Ln (1 + Z) = Z-Z ^ 2 / 2 + Z ^ 3 / 3 -..., so f (z) = ln (1 + Z) / z = 1-z / 2 + Z ^ 2 / 3 -..., z = 0 is de singular because there is no negative power term of Z in the expansion