Math 116: Study Guide - Chapter 7

1. Write the first five terms of the sequence. Two parts. Look at 7.1.1-22, 29-34
2. Simplify the ratio of the factorials: Two parts. Look at 7.1.69-78
3. Find the sum, given in summation notation. Two parts. Look at 7.1.79-90
4. Write the first five terms of the arithmetic sequence: Two parts. Look at 7.2.17-28
5. Find the nth partial sum of the arithmetic sequence. Look at 7.2.59-64
6. Find the sum of the arithmetic sequence, given in summation notation. Look at 7.2.65-78
7. Write the first five terms of the geometric sequence. Look at 7.3.11-26
8. Find the nth term of the geometric sequence. Look at 7.3.27-36
9. Find the sum of the geometric sequence, given in summation notation. Two parts, one finite, one infinite. Look at 7.3.55 -64 and 7.3.69-80
10. Evaluate a combination and a permutation. Two parts. Look at 7.5.13-18 and 7.6.33-38
11. Find the number of distinguishable permutations of a group of letters. Look at 7.6.43-46
12. Use the Binomial Expansion Theorem to expand and simplify the expression. Look at 7.5.23-40
13. Find the nth term of a binomial expansion. 7.5.49-56
14. Find a closed form for the sum. Look at the take home test
15. Write the first n rows of Pascal's triangle.

Notes:

• 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 530
• 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 75 points, the take-home portion of the test will be worth 25 points.
• The take-home portion of the test will be due on the day of the chapter exam.