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Chapter 8: Problem 65
Explain how to find the general term of an arithmetic sequence.
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What is the difference between a geometric sequence and an infinite geometric series?
a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is \(\frac{255}{365} \cdot \frac{364}{368} .\) Explain why this is so. (Ignore leap years and assume 365 days in a year.) b. If three people are selected at random, find the probability that they all have different birthdays. c. If three people are selected at random, find the probability that at least two of them have the same birthday. d. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday. e. How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
For the first 30 days of a flu outbreak, the number of students on your campus who become ill is increasing. Which is worse: The number of students with the flu is increasing arithmetically or is increasing geometrically? Explain your answer.
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (x-2)^{5} $$
Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(y^{3}-1\right)^{20} $$
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