## Math 116: Study Guide - Chapter 7

1. Write the first five terms of the sequence. Two parts. Look at 7.1.1 - 7.1.27*
2. Simplify the ratio of the factorials: Two parts. Look at 7.1.39 - 7.1.46* (one of these is directly from the text).
3. Find the sum, given in summation notation. Two parts. Look at 7.1.65 - 7.1.75*
4. Write the first five terms of the arithmetic sequence: Two parts. Look at 7.2.19 - 7.2.31*
5. Find the nth partial sum of the arithmetic sequence. Look at 7.2.55 - 7.2.61*
6. Find the sum of the arithmetic sequence, given in summation notation. Look at 7.2.63 - 7.2.69*
7. Write the first five terms of the geometric sequence. Look at 7.3.21 - 7.3.25*
8. Find the nth term of the geometric sequence. Look at 7.3.27 - 7.3.37*
9. Find the sum of the geometric sequence, given in summation notation. Two parts, one finite, one infinite. Look at 7.3.55 - 7.3.63* and 7.3.81 - 7.3.87*
10. Evaluate a combination and a permutation. Two parts. Look at 7.5.1 - 7.5.9* and 7.6.25 - 7.6.37*
11. Find the number of distinguishable permutations of a group of letters. Look at 7.6.47 - 7.6.50.
12. Find the probability. Two parts. Look at 7.7.7 - 7.7.20.
13. Use the Binomial Expansion Theorem to expand and simplify the expression. Look at 7.5.17 - 7.5.31*
14. Find the binomial in the difference quotient and simplify for the given function. Look at 7.5.41 - 7.5.47*
15. Find a closed form for the sum. Look at problems 7.4.19 - 7.4.33

### Notes:

• Every problem with a * after it is directly from the textbook.
• You may bring in a set of note cards with the following formulae:
• Arithmetic Sequences / Series: Common Difference, General Term, Sum of the first n terms (two formulas)
• Geometric Sequences / Series: Common Ratio, General Term, Sum of the first n terms, Sum of an infinite series
• Sum of the powers of the integers (1, n, n^2, n^3, n^4, n^5) - see page 558
• Formula for combination, permutation, and distinguishable permutations
• It would be wise to put each section of notes on a separate card, rather than trying to cram too much onto one card. Write large enough it's legible, and check for accuracy.
• The Binomial Expansion Theorem may NOT be on a note card.
• Because of the time it will take to work a mathematical induction problem, the mathematical induction problems have been moved to a take home test.
• The in-class portion of the test will be worth 70 points, the take-home portion of the test will be worth 30 points.
• The take-home portion of the test will be due on the day of the chapter exam.