Answer
Radius of convergence: 1
Work Step by Step
We are given $(1+x)^k$.
Write the binomial series expansion:
$(1+x)^k=\binom{k}{0}+\binom{k}{1}x+\binom{k}{2}x^2+\binom{k}{3}x^3+....+\binom{k}{k}x^k$
$=1+kx+\dfrac{k(k-1}{2!}x^2+\dfrac{k(k-1)(k-2)}{3!}+....+x^k$.
The radius of convergence for the series is 1.
