Chapter 10: Infinite Sequences and Series - Section 10.10 - The Binomial Series and Applications of Taylor Series - Exercises 10.10 - Page 633: 47

$\dfrac{x^3}{1-x} ; |x| \lt 1 $

Recall the Taylor series for $\dfrac{1}{1-x}= 1+x+x^2+......+x^n+.....; |x| \lt 1$ or, $=x^3+x^4+x^5+x^6+x^7+.....$ or, $=x^3(1+1+1+1+1....)$ or, $=x^3 (\dfrac{1}{1-x})$ or, $=\dfrac{x^3}{1-x} ; |x| \lt 1 $