Find the value of approximated to three decimals using the binomial theorem.
The value of each part must be determined and then added together. In order to use the binomial theorem, each number must be written in the form . In each case, is a whole number and is a decimal. Starting with the first number, . In expanded form, this is
Remember that and , so the coefficients of the first and last terms are both equal to 1. The remaining coefficients can be evaluated using .
The second number is less than 1, so a decimal needs to be subtracted from 1 to equal that number. In this case, , so the binomial theorem can be used. Remember that since we are subtracting.
Add the two values together: .
Rounded to three decimal places, the sum is 70.443.