## Calculus 8th Edition

Published by Cengage

# Chapter 11 - Infinite Sequences and Series - Review - Concept Check - Page 824: 12

#### 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 $1$.

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