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Chapter 8: Problem 36
Find each indicated sum. $$\sum_{i=2}^{4}\left(-\frac{1}{3}\right)^{i}$$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the Fundamental Counting Principle to determine the number of five- digit ZIP codes that are available to the U.S. Postal Service.
Some three-digit numbers, such as 101 and \(313,\) read the same forward and backward. If you select a number from all three digit numbers, find the probability that it will read the same forward and backward.
The group should select real-world situations where the Fundamental Counting Principle can be applied. These could involve the number of possible student ID numbers on your campus, the number of possible phone numbers in your community, the number of meal options at a local restaurant, the number of ways a person in the group can select outfits for class, the number of ways a condominium can be purchased in a nearby community, and so on. Once situations have been selected, group members should determine in how many ways each part of the task can be done. Group members will need to obtain menus, find out about telephone-digit requirements in the community, count shirts, pants, shoes in closets, visit condominium sales offices, and so on. Once the group reassembles, apply the Fundamental Counting Principle to determine the number of available options in each situation. Because these numbers may be quite large, use a calculator.
Prove that $$\left(\begin{array}{l}n \\\r\end{array}\right)-\left(\begin{array}{c}n \\\n-r\end{array}\right)$$.
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