Chapter 11.5, Problem 5P

To determine

To calculate:

Total number of ancestors does Kurt have in these $10$ generations.

Answer to Problem 5P

Total number of ancestors does Kurt have in these $10$ generations is $2046$ .

Explanation of Solution

Give information:

Kurt can trace is ancestors back though $10$ generations.

Calculation:

This is geometric series,

  $2+2^2+\mathrm{...}+2^{10}$

Using the formula for summing geometric series.

The sum is,

  $\begin{array}{l}\frac{2\left(1-2^{10}\right)}{1-2}\\ =2.1023\\ =2046\end{array}$

Therefore, Total number of ancestors does Kurt have in these $10$ generations is $2046$ .