Test 3 | Time: 1.5 hours |
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- Find the partial fraction decomposition of
- Identify the sequence (in the sum) as arithmetic, geometric, or
neither and find the sum:
- Identify the sequence as arithmetic, geometric, or
neither and find the sum of the first 25 terms using techniques
described in class. Round your answer to two decimal
places:
- In an arithmetic sequence, and .
- Find the formula which describes the nth term of this sequence.
- Using the formula found, write the first three terms of the sequence.

- Use mathematical induction to prove the given formula for every
positive integer n:
- An experiment consists of studying the number of boys and girls
in families with exactly 3 children. Let
**b**represent boys and**g**represent girls.- Describe the sample space that considers the ordering of the births of the 3 children.
- Describe the event that the family has exactly 2 girls.

- Consider the expression .
- Using the Binomial Theorem, write out the binomial expansion of the given expression and compute the third binomial coefficient by hand (show all steps).
- Using any method (calculator or by hand) find the rest of the coefficients, and simplify the expansion in the above part.

- A child has a set of different shaped plastic objects. There are
3 pyramids, 4 cubes, and 7 spheres.
- In how many ways can she arrange them in a row if they are all different colors?
- In how many distinguishable ways can they be arranged in a row if objects of the same shape are also the same color?

- One card is selected from a standard deck of 52 playing cards. What is the probability that the card is a heart or a two?
- From a group of 16 smokers and 20 nonsmokers, a researcher wants to randomly select 8 smokers and 8 nonsmokers for a study. In how many ways can the study group be selected?

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