Chapter 9.5, Problem 75E

To determine

To calculate: approximate value accurate to three decimal places using Binomial Theorem.

Answer to Problem 75E

  ${\left(2.99\right)}^{12}\approx 510568.785$

Explanation of Solution

Given information: ${\left(2.99\right)}^{12}$

Formula needed:Binomial theorem ${\left(x+y\right)}^n=C{}_0{x}^n+C{}_1{x}^{n-1}y+\cdot \cdot \cdot +C{}_r{x}^{n-r}{y}^r+\cdot \cdot \cdot +C{}_{n-1}{x}^1{y}^{n-1}+C{}_n{y}^n$ where, $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

Calculation:on rewriting given, ${\left(2.99\right)}^{12}={\left(3-0.01\right)}^{12}$

Here, $x=3,y=-0.01,\text{ and }n=12$

Apply binomial theorem,