Question

find the radius of the convergence of the Taylor series around x=0 for ln(1-x)

Answer 1

i guess it cannot be bigger than one, since log (0) i undefined.

Answer 2

we can compute it if you like

Answer 3

standard trick is to take the derivative get

\[-\frac{1}{1-x}\], write the expansion for that one and then integrate term by term

Answer 4

get
\[-\sum\frac{x^k}{k}\]

Answer 5

ratio test immediately tells you radius of convergence is 1