Complex variables-series

Find the function f(z) =log z given in a Taylor series around -1. Specify the maximum disk where this representation is valid
Thanks for your help

Starting with the geometric series 1/(1 - t) = Σ(n = 0 to ∞) t^n:

Integrate both sides from 0 to z:
-log(1 - z) = Σ(n = 0 to ∞) (-1)^n z^(n+1)/(n+1).
==> log(1 - z) = Σ(n = 0 to ∞) (-1)^(n+1) z^(n+1)/(n+1)
==> log(1 - z) = Σ(n = 1 to ∞) (-1)^n z^n/n
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So, log z
= log(1 - (z + 1))
= Σ(n = 1 to ∞) (-1)^n (z+1)^n/n.

This converges for |z+1| < 1.
So, R = 1.

I hope this helps!