Chapter 6.4, Problem 199E

In the following exercises, use the expansion ${(1+x)}^{1/3}=1+\frac{1}{3}x-\frac{1}{9}{x}^2+\frac{5}{81}{x}^3-\frac{10}{243}{x}^4+\mathrm{...}$ to write the first five terms (not necessarily a quartic polynomial) of each expression.

199. Use the approximation ${(1+x)}^{2/3}=1+\frac{2x}{3}-\frac{x^2}{9}-\frac{4x^3}{81}-\frac{7x^4}{243}-\frac{14x^5}{729}+\mathrm{...}$ for |x|<1 to approximate 2¹/3 = 2.2-2/3