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Chapter 8: Problem 44
Find the sum of each infinite geometric series. $$\sum_{i=1}^{\infty} 12(-0.7)^{i-1}$$
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What is a combination?
Exercises \(46-48\) will help you prepare for the material covered in ehe next section. Each exercise involves observing a pattern in the expanded form of the binomial expression \((a+b)^{n}\). $$\begin{array}{l} (a+b)^{1}=a+b \\ (a+b)^{2}=a^{2}+2 a b+b^{2} \\ (a+b)^{3}=a^{3}+3 a^{2} b+3 a b^{2}+b^{3} \\ (a+b)^{4}=a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4} \\ (a+b)^{5}=a^{5}+5 a^{4} b+10 a^{3} b^{2}+10 a^{2} b^{3}+5 a b^{4}+b^{5} \end{array}$$ Describe the pattern for the sum of the exponents on the variables in each term.
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 these six jokes be ranked from best to worst?
Exercises will help you prepare for the material covered in the next section. $$\text { Simplify: } \frac{k(k+1)(2 k+1)}{6}+(k+1)^{2}.$$
Use the formula for \(_{n} C_{r}\) to solve Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?
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