# How to find the radius of convergence of the given series

For the infinite series $\sum_{ j=0}^{\infty} a_n z^n$ the Radius of convergence is given by $$R=\lim_{n \rightarrow \infty} \left| \frac{a_n}{a_{ n+1}} \right|.$$ My question is, how to find the radius of convergence of $\sum_{ j=0}^{\infty} a_n (1-z) \cdot z^n ?$

• BTW if $\lim_{n\to \infty} |a_n/a_{n+1}$ exists then it is the radius of convergence. In general, use the Hadamard Radius Formula, – DanielWainfleet Feb 9 '17 at 0:21
$$\sum_{ j=0}^{\infty} a_n (1-z) \cdot z^n=(1-z)\sum_{ j=0}^{\infty} a_n \cdot z^n$$
The $(1-z)$ does not affect convergence.