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Chapter 8: Problem 42
Find the sum of each infinite geometric series. $$3-1+\frac{1}{3}-\frac{1}{9}+\cdots$$
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Exercises \(67-72\) are based on the following jokes about books: \(\cdot\) "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." - Groucho Marx \(\cdot\) "I recently bought a book of free verse. For \(\$ 12\)." \- George Carlin \(\cdot\) "If a word in the dictionary was misspelled, how would we know?" - Steven Wright \(\cdot\) "Encyclopedia is a Latin term. It means 'to paraphrase a term paper." - Greg Ray \(\cdot\) "A bookstore is one of the only pieces of evidence we have that people are still thinking." - Jerry Seinfeld \(\cdot\) "I honestly believe there is absolutely nothing like going to bed with a good book. Or a friend who's read one." \(-\)Phyllis Diller In how many ways can people select their three favorite jokes from these comments about books?
Exercises \(85-87\) will help you prepare for the material covered in the next section. Consider the sequence \(1,-2,4,-8,16, \ldots .\) Find \(\frac{a_{2}}{a_{1}}, \frac{a_{3}}{a_{2}}, \frac{a_{4}}{a_{3}}\)and \(\frac{a_{5}}{a_{4}} .\) What do you observe?
Solve by the method of your choice. A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?
What is the common difference in an arithmetic sequence?
Explain how to distinguish between permutation and combination problems.
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