What jobs that use the binomial theorem?

Answer 1

The binomial theorem allows you to express an expression of the form (y + x)^n as a power series. It is frequently put in the form of (1 + x)^n and the power series used as an approximation when x < < 1. When this is true you can make the approximation (1 + x)^n ~ 1 + nx , (the first two terms in the power series).This is very useful in analytical analysis of some problems and it is still used for that purpose. Before the rise of calculaters I used it frequently to estimate square roots and cube roots. For example, what is the square root of 84? Write sqrt(84) = sqrt(81 + 3) = 9 x sqrt(1 + 3/81) and this is approximately 9 (1 + (1/2)(3/81)) = 9 + 1/6 = 9.17 . You will see this is actually correct as rounded off to two decimals. Nowdays I just use the calculator so some of the usefullness of the binomial theorem has given way to technology.