Answer
The binomial series expansion of $(1+x)^k$ is $1+kx+\frac{k(k-1)}{2!}x^2+\frac{k(k-1)(k-2)}{3!}x^3+...+\frac{k(k-1)...(k-n+1)}{n!}x^n+....+b^{k-1}+b^k$ , the radius of convergence for the series is $1$.
Work Step by Step
The binomial series expansion of $(1+x)^k$ is $1+kx+\frac{k(k-1)}{2!}x^2+\frac{k(k-1)(k-2)}{3!}x^3+...+\frac{k(k-1)...(k-n+1)}{n!}x^n+....+b^{k-1}+b^k$ , the radius of convergence for the series is $1$.